更改

Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback.

Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback.

正反馈(加剧反馈，自我强化反馈) 是指在反馈循环中发生的一个过程，它加剧了小扰动的影响。即一个扰动对系统的影响包括扰动幅度的增大。也就是说，A会产生更多的B，而B又会产生更多的A，相反，一个系统中，变化的结果会减少或抵消变化的结果，这就是负反馈。

正反馈(加剧反馈，自我强化反馈) 是指在反馈循环中发生的一个过程，它加剧了小扰动的影响, 即一个扰动对系统的影响包括扰动幅度的增大。也就是说，A会产生更多的B，而B又会产生更多的A，相反，一个系统中，变化的结果会减少或抵消变化的结果，这就是负反馈。

<ref name=theorymodelling/> Both concepts play an important role in science and engineering, including biology, chemistry, and [[cybernetics]] .<br>

<ref name=theorymodelling/> Both concepts play an important role in science and engineering, including biology, chemistry, and [[cybernetics]] .<br>

Both concepts play an important role in science and engineering, including biology, chemistry, and cybernetics.

Both concepts play an important role in science and engineering, including biology, chemistry, and cybernetics.

这两个概念在科学和工程中发挥着重要作用，包括生物学、化学和控制论。

<ref name=theorymodelling/>这两个概念在科学和工程中发挥着重要作用，包括生物学、化学和控制论。

Mathematically, positive feedback is defined as a positive [[loop gain]] around a closed loop of cause and effect.<ref name=zuckerman/><ref name=theorymodelling>

Mathematically, positive feedback is defined as a positive [[loop gain]] around a closed loop of cause and effect.<ref name=zuckerman/><ref name=theorymodelling>

That is, positive feedback is in phase with the input, in the sense that it adds to make the input larger.

That is, positive feedback is in phase with the input, in the sense that it adds to make the input larger.

Positive feedback tends to cause system instability. When the loop gain is positive and above 1, there will typically be exponential growth, increasing oscillations, chaotic behavior or other divergences from equilibrium. System parameters will typically accelerate towards extreme values, which may damage or destroy the system, or may end with the system latched into a new stable state. Positive feedback may be controlled by signals in the system being filtered，damped or limited，or it can be cancelled or reduced by adding negative feedback.  

Positive feedback tends to cause system instability. When the loop gain is positive and above 1, there will typically be exponential growth, increasing oscillations, chaotic behavior or other divergences from equilibrium. System parameters will typically accelerate towards extreme values, which may damage or destroy the system, or may end with the system latched into a new stable state. Positive feedback may be controlled by signals in the system being filtered，damped or limited，or it can be cancelled or reduced by adding negative feedback.  

Positive feedback is used in digital electronics to force voltages away from intermediate voltages into '0' and '1' states. On the other hand, thermal runaway is a type of positive feedback that can destroy semiconductor junctions. Positive feedback in chemical reactions can increase the rate of reactions, and in some cases can lead to explosions. Positive feedback in mechanical design causes tipping-point, or 'over-centre', mechanisms to snap into position, for example in switches and locking pliers. Out of control, it can cause bridges to collapse. Positive feedback in economic systems can cause boom-then-bust cycles. A familiar example of positive feedback is the loud squealing or howling sound produced by audio feedback in public address systems: the microphone picks up sound from its own loudspeakers, amplifies it, and sends it through the speakers again.

Positive feedback is used in digital electronics to force voltages away from intermediate voltages into '0' and '1' states. On the other hand, thermal runaway is a type of positive feedback that can destroy semiconductor junctions. Positive feedback in chemical reactions can increase the rate of reactions, and in some cases can lead to explosions. Positive feedback in mechanical design causes tipping-point, or 'over-centre', mechanisms to snap into position, for example in switches and locking pliers. Out of control, it can cause bridges to collapse. Positive feedback in economic systems can cause boom-then-bust cycles. A familiar example of positive feedback is the loud squealing or howling sound produced by audio feedback in public address systems: the microphone picks up sound from its own loudspeakers, amplifies it, and sends it through the speakers again.

Positive feedback enhances or amplifies an effect by it having an influence on the process which gave rise to it. For example, when part of an electronic output signal returns to the input, and is in phase with it, the system [[Gain (electronics)|gain]] is increased.<ref>{{cite web|title=Positive feedback|url=http://www.oxforddictionaries.com/definition/english/positive-feedback|work=Oxford English Dictionary|publisher=Oxford University Press|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140302160045/http://www.oxforddictionaries.com/definition/english/positive-feedback|archivedate=2 March 2014}}<br>

Positive feedback enhances or amplifies an effect by it having an influence on the process which gave rise to it. For example, when part of an electronic output signal returns to the input, and is in phase with it, the system [[Gain (electronics)|gain]] is increased.<ref>{{cite web|title=Positive feedback|url=http://www.oxforddictionaries.com/definition/english/positive-feedback|work=Oxford English Dictionary|publisher=Oxford University Press|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140302160045/http://www.oxforddictionaries.com/definition/english/positive-feedback|archivedate=2 March 2014}}<br>

</ref> The feedback from the outcome to the originating process can be direct, or it can be via other state variables.<ref name=theorymodelling/> Such systems can give rich qualitative behaviors, but whether the feedback is instantaneously positive or negative in sign has an extremely important influence on the results.

</ref> The feedback from the outcome to the originating process can be direct, or it can be via other state variables.<ref name=theorymodelling/> Such systems can give rich qualitative behaviors, but whether the feedback is instantaneously positive or negative in sign has an extremely important influence on the results.

<ref name=theorymodelling/> Positive feedback reinforces and negative feedback moderates the original process. ''Positive'' and ''negative'' in this sense refer to loop gains greater than or less than zero, and do not imply any [[value judgement]]s as to the desirability of the outcomes or effects.<ref>{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref>  A key feature of positive feedback is thus that small disturbances get bigger. When a change occurs in a system, positive feedback causes further change, in the same direction.

<ref name=theorymodelling/> Positive feedback reinforces and negative feedback moderates the original process. ''Positive'' and ''negative'' in this sense refer to loop gains greater than or less than zero, and do not imply any [[value judgement]]s as to the desirability of the outcomes or effects.<ref>{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref>  A key feature of positive feedback is thus that small disturbances get bigger. When a change occurs in a system, positive feedback causes further change, in the same direction.

正反馈强化原过程，负反馈调节原过程。''正''和''负''在这个意义上指的是大于或小于零的循环收益，并不意味着对结果或效果的可取性有任何价值判断。

<ref name=theorymodelling/> 正反馈强化原过程，负反馈调节原过程。''正''和''负''在这个意义上指的是大于或小于零的循环收益，并不意味着对结果或效果的可取性有任何价值判断。

If the functions A and B are linear and AB is smaller than unity, then the overall system gain from the input to output is finite, but can be very large as AB approaches unity.<ref name=smith> Electronics circuits and devices second edition.  Ralph J. Smith</ref>  In that case, it can be shown that the overall or "closed loop" gain from input to output is:

If the functions A and B are linear and AB is smaller than unity, then the overall system gain from the input to output is finite, but can be very large as AB approaches unity.<ref name=smith> Electronics circuits and devices second edition.  Ralph J. Smith</ref>  In that case, it can be shown that the overall or "closed loop" gain from input to output is:

如果函数A和B是线性的，且AB小于1，那么系统从输入到输出的整体增益是有限的，但当AB接近1时，系统的增益可以非常大。

如果函数A和B是线性的，且AB小于1，那么系统从输入到输出的整体增益是有限的，但当AB接近1时，系统的增益可以非常大。<ref name=smith> Electronics circuits and devices second edition.  Ralph J. Smith</ref> 

在这种情况下，可以表明从输入到输出的整体或 "闭环 "增益为：

在这种情况下，可以表明从输入到输出的整体或 "闭环 "增益为：

Positive feedback does not necessarily imply instability of an equilibrium, for example stable ''on'' and ''off'' states may exist in positive-feedback architectures.<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>

Positive feedback does not necessarily imply instability of an equilibrium, for example stable ''on'' and ''off'' states may exist in positive-feedback architectures.<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>

正反馈并不一定意味着平衡的不稳定性，例如，在正反馈结构中可能存在稳定的开关状态。

正反馈并不一定意味着平衡的不稳定性，例如，在正反馈结构中可能存在稳定的开关状态。.<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>

 

=== Hysteresis ===

=== Hysteresis ===

{{main|Hysteresis}}

{{main|Hysteresis}}

Hysteresis causes the output value to depend on the history of the input

Hysteresis causes the output value to depend on the history of the input

[[File:Op-Amp Schmitt Trigger.svg|thumb|In a [[Schmitt trigger]] circuit, feedback to the non-inverting input of an amplifier pushes the output directly away from the applied voltage towards the maximum or minimum voltage the amplifier can generate.]]

[[File:Op-Amp Schmitt Trigger.svg|thumb|In a [[Schmitt trigger]] circuit, feedback to the non-inverting input of an amplifier pushes the output directly away from the applied voltage towards the maximum or minimum voltage the amplifier can generate.]]

::"Positive feedback loops are sources of growth, explosion, erosion, and collapse in systems. A system with an unchecked positive loop ultimately will destroy itself. That’s why there are so few of them. Usually a negative loop will kick in sooner or later."<ref name=meadows>

::"Positive feedback loops are sources of growth, explosion, erosion, and collapse in systems. A system with an unchecked positive loop ultimately will destroy itself. That’s why there are so few of them. Usually a negative loop will kick in sooner or later."<ref name=meadows>

“正反馈循环是系统增长、爆炸、侵蚀和崩溃的源头。如果一个系统的正循环不受控制，最终将会自我毁灭。这就是为什么很少有这样的系统。通常情况下，负面循环迟早会发生。”

“正反馈循环是系统增长、爆炸、侵蚀和崩溃的源头。如果一个系统的正循环不受控制，最终将会自我毁灭。这就是为什么很少有这样的系统。通常情况下，负面循环迟早会发生。”<ref name=meadows>

Donella Meadows, [http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf ''Leverage Points: Places to Intervene in a System''] {{webarchive|url=https://web.archive.org/web/20131008160618/http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf |date=2013-10-08 }}, 1999</ref>

Donella Meadows, [http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf ''Leverage Points: Places to Intervene in a System''] {{webarchive|url=https://web.archive.org/web/20131008160618/http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf |date=2013-10-08 }}, 1999</ref>

The terms positive and negative were first applied to feedback before World War II. The idea of positive feedback was already current in the 1920s with the introduction of the regenerative circuit.

The terms positive and negative were first applied to feedback before World War II. The idea of positive feedback was already current in the 1920s with the introduction of the regenerative circuit.

Friis & Jensen (1924) described regeneration in a set of electronic amplifiers as a case where the "feed-back" action is positive in contrast to negative feed-back action, which they mention only in passing. Harold Stephen Black's classic 1934 paper first details the use of negative feedback in electronic amplifiers. According to Black:

Friis & Jensen (1924) described regeneration in a set of electronic amplifiers as a case where the "feed-back" action is positive in contrast to negative feed-back action, which they mention only in passing. Harold Stephen Black's classic 1934 paper first details the use of negative feedback in electronic amplifiers. According to Black:

Friis & Jensen(1924)将一组电子放大器中的再生描述为 "回馈 "作用是正的情况，与负回馈作用相反，他们只是顺便提到了负回馈。哈罗德•斯蒂芬•布莱克（Harold Stephen Black）在1934年的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法：

Friis & Jensen(1924)将一组电子放大器中的再生描述为 "回馈 "作用是正的情况，与他们顺便提到的负回馈作用相反。哈罗德•斯蒂芬•布莱克（Harold Stephen Black）在1934年的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法：

Regenerative circuits were invented and patented in 1914 for the amplification and reception of very weak radio signals. Carefully controlled positive feedback around a single transistor amplifier can multiply its gain by 1,000 or more. Therefore, a signal can be amplified 20,000 or even 100,000 times in one stage, that would normally have a gain of only 20 to 50. The problem with regenerative amplifiers working at these very high gains is that they easily become unstable and start to oscillate. The radio operator has to be prepared to tweak the amount of feedback fairly continuously for good reception. Modern radio receivers use the superheterodyne design, with many more amplification stages, but much more stable operation and no positive feedback.

Regenerative circuits were invented and patented in 1914 for the amplification and reception of very weak radio signals. Carefully controlled positive feedback around a single transistor amplifier can multiply its gain by 1,000 or more. Therefore, a signal can be amplified 20,000 or even 100,000 times in one stage, that would normally have a gain of only 20 to 50. The problem with regenerative amplifiers working at these very high gains is that they easily become unstable and start to oscillate. The radio operator has to be prepared to tweak the amount of feedback fairly continuously for good reception. Modern radio receivers use the superheterodyne design, with many more amplification stages, but much more stable operation and no positive feedback.

The oscillation that can break out in a regenerative radio circuit is used in electronic oscillators. By the use of tuned circuits or a piezoelectric crystal (commonly quartz), the signal that is amplified by the positive feedback remains linear and sinusoidal. There are several designs for such harmonic oscillators, including the Armstrong oscillator, Hartley oscillator, Colpitts oscillator, and the Wien bridge oscillator. They all use positive feedback to create oscillations.

The oscillation that can break out in a regenerative radio circuit is used in electronic oscillators. By the use of tuned circuits or a piezoelectric crystal (commonly quartz), the signal that is amplified by the positive feedback remains linear and sinusoidal. There are several designs for such harmonic oscillators, including the Armstrong oscillator, Hartley oscillator, Colpitts oscillator, and the Wien bridge oscillator. They all use positive feedback to create oscillations.

在再生无线电电路中能爆发出的振荡被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英)，经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计，包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。

在再生无线电电路中能爆发出的振荡被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英)，经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计，包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref>

 

Many electronic circuits, especially amplifiers, incorporate negative feedback. This reduces their gain, but improves their linearity, input impedance, output impedance, and bandwidth, and stabilises all of these parameters, including the closed-loop gain. These parameters also become less dependent on the details of the amplifying device itself, and more dependent on the feedback components, which are less likely to vary with manufacturing tolerance, age and temperature. The difference between positive and negative feedback for AC signals is one of phase: if the signal is fed back out of phase, the feedback is negative and if it is in phase the feedback is positive. One problem for amplifier designers who use negative feedback is that some of the components of the circuit will introduce phase shift in the feedback path. If there is a frequency (usually a high frequency) where the phase shift reaches 180°, then the designer must ensure that the amplifier gain at that frequency is very low (usually by low-pass filtering). If the loop gain (the product of the amplifier gain and the extent of the positive feedback) at any frequency is greater than one, then the amplifier will oscillate at that frequency (Barkhausen stability criterion). Such oscillations are sometimes called parasitic oscillations. An amplifier that is stable in one set of conditions can break into parasitic oscillation in another. This may be due to changes in temperature, supply voltage, adjustment of front-panel controls, or even the proximity of a person or other conductive item.

Many electronic circuits, especially amplifiers, incorporate negative feedback. This reduces their gain, but improves their linearity, input impedance, output impedance, and bandwidth, and stabilises all of these parameters, including the closed-loop gain. These parameters also become less dependent on the details of the amplifying device itself, and more dependent on the feedback components, which are less likely to vary with manufacturing tolerance, age and temperature. The difference between positive and negative feedback for AC signals is one of phase: if the signal is fed back out of phase, the feedback is negative and if it is in phase the feedback is positive. One problem for amplifier designers who use negative feedback is that some of the components of the circuit will introduce phase shift in the feedback path. If there is a frequency (usually a high frequency) where the phase shift reaches 180°, then the designer must ensure that the amplifier gain at that frequency is very low (usually by low-pass filtering). If the loop gain (the product of the amplifier gain and the extent of the positive feedback) at any frequency is greater than one, then the amplifier will oscillate at that frequency (Barkhausen stability criterion). Such oscillations are sometimes called parasitic oscillations. An amplifier that is stable in one set of conditions can break into parasitic oscillation in another. This may be due to changes in temperature, supply voltage, adjustment of front-panel controls, or even the proximity of a person or other conductive item.

许多电子电路，特别是放大器，都采用了负反馈。这降低了它们的增益，但改善了它们的线性度、输入阻抗、输出阻抗和带宽，并稳定了所有这些参数，包括闭环增益。这些参数也变得不那么依赖于放大器件本身的细节，而更多地依赖于反馈元件，因为反馈元件不太可能随着制造公差、年龄和温度而变化。交流信号的正反馈和负反馈的区别在于相位问题：如果信号反馈失相，则反馈为负，如果相位一致，则反馈为正。对于使用负反馈的放大器设计者来说，有一个问题是，电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°，那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波)。如果任何频率下的环增益（放大器增益与正反馈程度的乘积）大于1，那么放大器将在该频率下发生振荡（巴克豪森稳定性准则）。这种振荡有时被称为寄生振荡。在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化，前面板控制的调整，甚至是人或其他导电物品的接近。

许多电子电路，特别是放大器，都采用了负反馈。这降低了它们的增益，但改善了它们的线性度、输入阻抗、输出阻抗和带宽，并稳定了所有这些参数，包括闭环增益。这些参数也变得不那么依赖于放大器件本身的细节，而更多地依赖于反馈元件，因为反馈元件不太可能随着制造公差、使用年限和温度而变化。交流信号的正反馈和负反馈的区别在于相位问题：如果信号反馈失相，则反馈为负，如果相位一致，则反馈为正。对于使用负反馈的放大器设计者来说，有一个问题是，电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°，那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波)。如果任何频率下的环增益（放大器增益与正反馈程度的乘积）大于1，那么放大器将在该频率下发生振荡（巴克豪森稳定性准则）。这种振荡有时被称为寄生振荡。在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化，前面板控制的调整，甚至是人或其他导电物品的接近。

Amplifiers may oscillate gently in ways that are hard to detect without an oscilloscope, or the oscillations may be so extensive that only a very distorted or no required signal at all gets through, or that damage occurs. Low frequency parasitic oscillations have been called 'motorboating' due to the similarity to the sound of a low-revving exhaust note.

Amplifiers may oscillate gently in ways that are hard to detect without an oscilloscope, or the oscillations may be so extensive that only a very distorted or no required signal at all gets through, or that damage occurs. Low frequency parasitic oscillations have been called 'motorboating' due to the similarity to the sound of a low-revving exhaust note.

Thermal runaway occurs in electronic systems because some aspect of a circuit is allowed to pass more current when it gets hotter, then the hotter it gets, the more current it passes, which heats it some more and so it passes yet more current. The effects are usually catastrophic for the device in question. If devices have to be used near to their maximum power-handling capacity, and thermal runaway is possible or likely under certain conditions, improvements can usually be achieved by careful design.

Thermal runaway occurs in electronic systems because some aspect of a circuit is allowed to pass more current when it gets hotter, then the hotter it gets, the more current it passes, which heats it some more and so it passes yet more current. The effects are usually catastrophic for the device in question. If devices have to be used near to their maximum power-handling capacity, and thermal runaway is possible or likely under certain conditions, improvements can usually be achieved by careful design.

[[File:Technics SL-1210MK2.jpg|thumb|left|A phonograph turntable is prone to acoustic feedback.]]

[[File:Technics SL-1210MK2.jpg|thumb|left|A phonograph turntable is prone to acoustic feedback.]]

其中一个例子是分娩时宫缩的发生，称为弗格森反射。当宫缩发生时，激素催产素会引起神经刺激，刺激下丘脑产生更多的催产素，从而增加子宫收缩。这就导致宫缩的幅度和频率增加。

其中一个例子是分娩时宫缩的发生，称为弗格森反射。当宫缩发生时，激素催产素会引起神经刺激，刺激下丘脑产生更多的催产素，从而增加子宫收缩。这就导致宫缩的幅度和频率增加。

* Another example is the process of [[Coagulation|blood clotting]]. The loop is initiated when injured tissue releases signal chemicals that activate platelets in the blood. An activated platelet releases chemicals to activate more platelets, causing a rapid cascade and the formation of a blood clot.<ref name=Guyton1991/>{{rp|pages=392–394}}

* Another example is the process of [[Coagulation|blood clotting]]. The loop is initiated when injured tissue releases signal chemicals that activate platelets in the blood. An activated platelet releases chemicals to activate more platelets, causing a rapid cascade and the formation of a blood clot.<ref name=Guyton1991/>{{rp|pages=392–394}}

Positive feedback is a well studied phenomenon in gene regulation, where it is most often associated with [[bistability]]. Positive feedback occurs when a gene activates itself directly or indirectly via a double negative feedback loop. Genetic engineers have constructed and tested simple positive feedback networks in bacteria to demonstrate the concept of bistability.<ref name=Hasty2002/> A classic example of positive feedback is the [[lac operon]] in ''E. coli''. Positive feedback plays an integral role in cellular differentiation, development, and cancer progression, and therefore, positive feedback in gene regulation can have significant physiological consequences. Random motions in [[molecular dynamics]] coupled with positive feedback can trigger interesting effects, such as create population of phenotypically different cells from the same parent cell.<ref name=Veening2008/> This happens because noise can become amplified by positive feedback. Positive feedback can also occur in other forms of [[cell signaling]], such as enzyme kinetics or metabolic pathways.<ref name=Christoph2001/>

Positive feedback is a well studied phenomenon in gene regulation, where it is most often associated with [[bistability]]. Positive feedback occurs when a gene activates itself directly or indirectly via a double negative feedback loop. Genetic engineers have constructed and tested simple positive feedback networks in bacteria to demonstrate the concept of bistability.<ref name=Hasty2002/> A classic example of positive feedback is the [[lac operon]] in ''E. coli''. Positive feedback plays an integral role in cellular differentiation, development, and cancer progression, and therefore, positive feedback in gene regulation can have significant physiological consequences. Random motions in [[molecular dynamics]] coupled with positive feedback can trigger interesting effects, such as create population of phenotypically different cells from the same parent cell.<ref name=Veening2008/> This happens because noise can become amplified by positive feedback. Positive feedback can also occur in other forms of [[cell signaling]], such as enzyme kinetics or metabolic pathways.<ref name=Christoph2001/>

正反馈是基因调控中研究得很好的一种现象，其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时，就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络，以证明双稳态的概念。

正反馈是基因调控中研究得很好的一种现象，其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时，就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络，以证明双稳态的概念。<ref name=Hasty2002/>

正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用，因此，基因调控中的正反馈可以产生显著的生理后果。分子动力学中的随机运动加上正反馈可以引发有趣的效应，例如从同一母细胞中产生表型不同的细胞群。

正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用，因此，基因调控中的正反馈可以产生显著的生理后果。分子动力学中的随机运动加上正反馈可以引发有趣的效应，例如从同一母细胞中产生表型不同的细胞群。<ref name=Veening2008/>

这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中，如酶动力学或代谢途径。

这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中，如酶动力学或代谢途径。<ref name=Christoph2001/>

==== In evolutionary biology ====

==== In evolutionary biology ====

Positive feedback loops have been used to describe aspects of the dynamics of change in biological [[evolution]].  For example, beginning at the macro level, [[Alfred J. Lotka]] (1945) argued that the evolution of the species was most essentially a matter of selection that fed back energy flows to capture more and more energy for use by living systems.<ref name=Lotka1945/> At the human level, [[Richard D. Alexander]] (1989) proposed that social competition between and within human groups fed back to the selection of intelligence thus constantly producing more and more refined human intelligence. <ref name=Alexander1989/> [[Bernard Crespi|Crespi]] (2004) discussed several other examples of positive feedback loops in evolution.<ref name=Crespi2004/>  The analogy of [[Evolutionary arms race]]s provide further examples of positive feedback in biological systems.<ref name=Blindwatchmaker/>

Positive feedback loops have been used to describe aspects of the dynamics of change in biological [[evolution]].  For example, beginning at the macro level, [[Alfred J. Lotka]] (1945) argued that the evolution of the species was most essentially a matter of selection that fed back energy flows to capture more and more energy for use by living systems.<ref name=Lotka1945/> At the human level, [[Richard D. Alexander]] (1989) proposed that social competition between and within human groups fed back to the selection of intelligence thus constantly producing more and more refined human intelligence. <ref name=Alexander1989/> [[Bernard Crespi|Crespi]] (2004) discussed several other examples of positive feedback loops in evolution.<ref name=Crespi2004/>  The analogy of [[Evolutionary arms race]]s provide further examples of positive feedback in biological systems.<ref name=Blindwatchmaker/>

正反馈循环被用来描述生物进化中变化动态的各个方面。 例如，在宏观层面，阿尔弗雷德•J•洛特卡Alfred J. Lotka(1945)认为，物种的进化最本质上是一个选择问题，它反馈了能量流，以获取越来越多的能量供生物系统使用。在人类层面，理查德•D•亚历山大 Richard D. Alexander(1989)提出，人类群体之间和群体内部的社会竞争反馈到智力的选择上，从而不断产生更多、更完善的人类智力。 Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子。进化军备竞赛的类比给生物系统中的正反馈提供了进一步的例子。

正反馈循环被用来描述生物进化中变化动态的各个方面。 例如，在宏观层面，阿尔弗雷德•J•洛特卡Alfred J. Lotka(1945)认为，物种的进化最本质上是一个选择问题，它反馈了能量流，以获取越来越多的能量供生物系统使用。<ref name=Lotka1945/>在人类层面，理查德•D•亚历山大 Richard D. Alexander(1989)提出，人类群体之间和群体内部的社会竞争反馈到智力的选择上，从而不断产生更多、更完善的人类智力。 <ref name=Alexander1989/> Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子。进化军备竞赛的类比给生物系统中的正反馈提供了进一步的例子。<ref name=Blindwatchmaker/>

It has been shown that changes in [[biodiversity]] through the [[Phanerozoic]] correlate much better with hyperbolic model (widely used in [[demography]] and [[macrosociology]]) than with [[Exponential growth|exponential]] and [[Logistic function|logistic]] models (traditionally used in [[population biology]] and extensively applied to [[fossil]] [[biodiversity]] as well). The latter models imply that changes in diversity are guided by a first-order positive feedback (more ancestors, more descendants) and/or a [[negative feedback]] arising from resource limitation.  Hyperbolic model implies a second-order positive feedback. The hyperbolic pattern of the [[world population growth]] has been demonstrated (see below) to arise from a second-order positive feedback between the population size and the rate of [[technological growth]]. The hyperbolic character of biodiversity growth can be similarly accounted for by a positive feedback between the diversity and community structure complexity. It has been suggested that the similarity between the curves of [[biodiversity]] and human population probably comes from the fact that both are derived from the interference of the hyperbolic trend (produced by the positive feedback) with cyclical and stochastic dynamics.<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref>

It has been shown that changes in [[biodiversity]] through the [[Phanerozoic]] correlate much better with hyperbolic model (widely used in [[demography]] and [[macrosociology]]) than with [[Exponential growth|exponential]] and [[Logistic function|logistic]] models (traditionally used in [[population biology]] and extensively applied to [[fossil]] [[biodiversity]] as well). The latter models imply that changes in diversity are guided by a first-order positive feedback (more ancestors, more descendants) and/or a [[negative feedback]] arising from resource limitation.  Hyperbolic model implies a second-order positive feedback. The hyperbolic pattern of the [[world population growth]] has been demonstrated (see below) to arise from a second-order positive feedback between the population size and the rate of [[technological growth]]. The hyperbolic character of biodiversity growth can be similarly accounted for by a positive feedback between the diversity and community structure complexity. It has been suggested that the similarity between the curves of [[biodiversity]] and human population probably comes from the fact that both are derived from the interference of the hyperbolic trend (produced by the positive feedback) with cyclical and stochastic dynamics.<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref>

研究表明，在显生宙，生物多样性的变化与双曲模型（广泛用于人口学和宏观社会学）的相关性要比指数模型和逻辑模型（传统上用于人口生物学，并广泛用于生物多样性化石）的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈（更多的祖先，更多的后代）和/或资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明（见下文），源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为，生物多样性和人口曲线之间的相似性可能来自这样一个事实，即两者都是由双曲趋势(由正反馈产生)与周期性和随机性动态的干扰而产生的。

研究表明，在显生宙，生物多样性的变化与双曲模型（广泛用于人口学和宏观社会学）的相关性要比指数模型和逻辑逻辑斯谛（传统上用于人口生物学，并广泛用于生物多样性化石）的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈（更多的祖先，更多的后代）和/或资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明（见下文），源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为，生物多样性和人口曲线之间的相似性可能来自这样一个事实，即两者都是由双曲趋势(由正反馈产生)与周期性和随机性动态的干扰而产生的。

A [[cytokine storm]], or '''hypercytokinemia''' is a potentially fatal immune reaction consisting of a positive feedback loop between [[cytokine]]s and [[immune cell]]s, with highly elevated levels of various cytokines.<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068  | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref> In normal immune function, positive feedback loops can be utilized to enhance the action of B lymphocytes. When a B cell binds its antibodies to an antigen and becomes activated, it begins releasing antibodies and secreting a complement protein called C3. Both C3 and a B cell's antibodies can bind to a pathogen, and when a B cell has its antibodies bind to a pathogen with C3, it speeds up that B cell's secretion of more antibodies and more C3, thus creating a positive feedback loop.<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref>

A [[cytokine storm]], or '''hypercytokinemia''' is a potentially fatal immune reaction consisting of a positive feedback loop between [[cytokine]]s and [[immune cell]]s, with highly elevated levels of various cytokines.<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068  | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref> In normal immune function, positive feedback loops can be utilized to enhance the action of B lymphocytes. When a B cell binds its antibodies to an antigen and becomes activated, it begins releasing antibodies and secreting a complement protein called C3. Both C3 and a B cell's antibodies can bind to a pathogen, and when a B cell has its antibodies bind to a pathogen with C3, it speeds up that B cell's secretion of more antibodies and more C3, thus creating a positive feedback loop.<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref>

细胞因子风暴，或称高细胞因子血症，是一种潜在的致命性免疫反应，由细胞因子和免疫细胞之间的正反馈环组成，各种细胞因子水平高度升高[36]在正常的免疫功能中，可以利用正反馈环来增强B淋巴细胞的作用。当B细胞将其抗体与抗原结合并被激活后，就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合，当B细胞的抗体与C3结合后，就会加快该B细胞分泌更多的抗体和更多的C3，从而形成一个正反馈循环。

细胞因子风暴，或称高细胞因子血症，是一种潜在的致命性免疫反应，由细胞因子和免疫细胞之间的正反馈环组成，各种细胞因子水平高度升高[36]在正常的免疫功能中，可以利用正反馈环来增强B淋巴细胞的作用。<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068  | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref>当B细胞将其抗体与抗原结合并被激活后，就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合，当B细胞的抗体与C3结合后，就会加快该B细胞分泌更多的抗体和更多的C3，从而形成一个正反馈循环。<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref>

==== Cell death ====

==== Cell death ====

[[Apoptosis]] is a [[caspase]]-mediated process of cellular death, whose aim is the removal of long-lived or damaged cells. A failure of this process has been implicated in prominent conditions such as [[cancer]] or [[Parkinson's disease]]. The very core of the apoptotic process is the auto-activation of caspases, which may be modeled via a positive-feedback loop. This positive feedback exerts an auto-activation of the [[effector caspase]] by means of intermediate caspases. When isolated from the rest of apoptotic pathway, this positive-feedback presents only one stable steady state, regardless of the number of intermediate activation steps of the effector caspase.<ref name="ReferenceA"/> When this core process is complemented with inhibitors and enhancers of caspases effects, this process presents bistability, thereby modeling the alive and dying states of a cell.<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref>

[[Apoptosis]] is a [[caspase]]-mediated process of cellular death, whose aim is the removal of long-lived or damaged cells. A failure of this process has been implicated in prominent conditions such as [[cancer]] or [[Parkinson's disease]]. The very core of the apoptotic process is the auto-activation of caspases, which may be modeled via a positive-feedback loop. This positive feedback exerts an auto-activation of the [[effector caspase]] by means of intermediate caspases. When isolated from the rest of apoptotic pathway, this positive-feedback presents only one stable steady state, regardless of the number of intermediate activation steps of the effector caspase.<ref name="ReferenceA"/> When this core process is complemented with inhibitors and enhancers of caspases effects, this process presents bistability, thereby modeling the alive and dying states of a cell.<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref>

细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程，其目的是清除长寿或受损的细胞。这一过程的失败与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活，它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时，无论效应子胱天蛋白酶的中间激活步骤的数量如何，这种正反馈仅呈现一种稳定的稳态。

细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程，其目的是清除长寿或受损的细胞。这一过程的失败与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活，它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时，无论效应子胱天蛋白酶的中间激活步骤的数量如何，这种正反馈仅呈现一种稳定的稳态。<ref name="ReferenceA"/>

当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时，该过程呈现双稳态，从而模拟细胞的存活和死亡状态。

当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时，该过程呈现双稳态，从而模拟细胞的存活和死亡状态。

Winner (1996) described gifted children as driven by positive feedback loops involving setting their own learning course, this feeding back satisfaction, thus further setting their learning goals to higher levels and so on.<ref name=Winner1996/>  Winner termed this positive feedback loop as a "rage to master."  Vandervert (2009a, 2009b) proposed that the [[child prodigy]] can be explained in terms of a positive feedback loop between the output of thinking/performing in [[working memory]], which then is fed to the [[cerebellum]] where it is streamlined, and then fed back to working memory thus steadily increasing the quantitative and qualitative output of working memory.<ref name=Vandervert2009a/><ref name=Vandervert2009b/>  Vandervert also argued that this working memory/cerebellar positive feedback loop was responsible for [[language]] evolution in working memory.

Winner (1996) described gifted children as driven by positive feedback loops involving setting their own learning course, this feeding back satisfaction, thus further setting their learning goals to higher levels and so on.<ref name=Winner1996/>  Winner termed this positive feedback loop as a "rage to master."  Vandervert (2009a, 2009b) proposed that the [[child prodigy]] can be explained in terms of a positive feedback loop between the output of thinking/performing in [[working memory]], which then is fed to the [[cerebellum]] where it is streamlined, and then fed back to working memory thus steadily increasing the quantitative and qualitative output of working memory.<ref name=Vandervert2009a/><ref name=Vandervert2009b/>  Vandervert also argued that this working memory/cerebellar positive feedback loop was responsible for [[language]] evolution in working memory.

温纳（Winner，1996）将有天赋的孩子描述为受到正反馈循环的驱动，这些反馈循环涉及设置自己的学习课程，反馈自己的满意程度，从而进一步将他们的学习目标提高到更高水平等等。

温纳（Winner，1996）将有天赋的孩子描述为受到正反馈循环的驱动，这些反馈循环涉及设置自己的学习课程，反馈自己的满意程度，从而进一步将他们的学习目标提高到更高水平等等。<ref name=Winner1996/>

Winner将这种正反馈循环称为 "愤怒的掌握"。 Vandervert(2009a，2009b)提出，神童可以用工作记忆中的思维/表现的输出之间的正反馈回路来解释，工作记忆中的思维/表现的输出被反馈到小脑，在那里被精简，然后再反馈到工作记忆中，从而稳定地增加工作记忆的数量和质量输出。

Winner将这种正反馈循环称为 "愤怒的掌握"。 Vandervert(2009a，2009b)提出，神童可以用工作记忆中的思维/表现的输出之间的正反馈回路来解释，工作记忆中的思维/表现的输出被反馈到小脑，在那里被精简，然后再反馈到工作记忆中，从而稳定地增加工作记忆的数量和质量输出。<ref name=Vandervert2009a/><ref name=Vandervert2009b/>

=== In economics ===

=== In economics ===

Product recommendations and information about past purchases have been shown to influence consumers choices significantly whether it is for music, movie, book, technological, and other type of products. Social influence often induces a rich-get-richer phenomenon ([[Matthew effect]]) where popular products tend to become even more popular.<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref>

Product recommendations and information about past purchases have been shown to influence consumers choices significantly whether it is for music, movie, book, technological, and other type of products. Social influence often induces a rich-get-richer phenomenon ([[Matthew effect]]) where popular products tend to become even more popular.<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref>

事实证明，产品推荐和过去购买的信息对消费者的选择影响很大，无论是音乐、电影、书籍、技术还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象（马太效应），即热门产品往往会变得更加受欢迎。

事实证明，产品推荐和过去购买的信息对消费者的选择影响很大，无论是音乐、电影、书籍、技术还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象（马太效应），即热门产品往往会变得更加受欢迎。<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref>

====Market dynamics====

====Market dynamics====

According to the theory of [[reflexivity (social theory)|reflexivity]] advanced by [[George Soros]], price changes are driven by a positive feedback process whereby investors' expectations are influenced by price movements so their behaviour acts to reinforce movement in that direction until it becomes unsustainable, whereupon the feedback drives prices in the opposite direction.<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref>

According to the theory of [[reflexivity (social theory)|reflexivity]] advanced by [[George Soros]], price changes are driven by a positive feedback process whereby investors' expectations are influenced by price movements so their behaviour acts to reinforce movement in that direction until it becomes unsustainable, whereupon the feedback drives prices in the opposite direction.<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref>

根据乔治•索罗斯 George Soros提出的反射性理论，价格变化是由一个正反馈过程驱动的，即投资者的预期受到价格变动的影响，因此他们的行为会强化这个方向的运动，直到它变得不可持续，于是反馈推动价格向相反的方向发展。

根据乔治•索罗斯 George Soros提出的反射性理论，价格变化是由一个正反馈过程驱动的，即投资者的预期受到价格变动的影响，因此他们的行为会强化这个方向的运动，直到它变得不可持续，于是反馈推动价格向相反的方向发展。<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref>

==== Systemic risk ====

==== Systemic risk ====

Agriculture and human population can be considered to be in a positive feedback mode, which means that one drives the other with increasing intensity. It is suggested that this positive feedback system will end sometime with a catastrophe, as modern agriculture is using up all of the easily available phosphate and is resorting to highly efficient monocultures which are more susceptible to systemic risk.

Agriculture and human population can be considered to be in a positive feedback mode, which means that one drives the other with increasing intensity. It is suggested that this positive feedback system will end sometime with a catastrophe, as modern agriculture is using up all of the easily available phosphate and is resorting to highly efficient monocultures which are more susceptible to systemic risk.