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[[迟滞]]，即起点影响系统的终点的现象，可以通过正反馈产生。当反馈循环的增益高于1时，那么输出就会远离输入：如果大于输入，则向最近的正极限移动，而如果小于输入，则向最近的负极限移动。

[[迟滞]]，即起点影响系统的终点的现象，可以通过正反馈产生。当反馈循环的增益高于1时，那么输出就会远离输入：如果大于输入，则向最近的正极限移动，而如果小于输入，则向最近的负极限移动。

Once it reaches the limit, it will be stable. However, if the input goes past the limit,{{clarify|date=June 2012}} then the feedback will change sign{{dubious|date=June 2012}} and the output will move in the opposite direction until it hits the opposite limit. The system therefore shows [[bistability|bistable]] behaviour.

Once it reaches the limit, it will be stable. However, if the input goes past the limit,{{clarify|date=June 2012}} then the feedback will change sign{{dubious|date=June 2012}} and the output will move in the opposite direction until it hits the opposite limit. The system therefore shows [[bistability|bistable]] behavior.

== Terminology ==

== Terminology ==

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.

再生电路于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>，用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈，可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此，一个信号可以在一个阶段被放大20000甚至100000倍，而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定，开始振荡。无线电操作员必须不断地调整反馈量，以获得良好的接收效果。而现代无线电接收机采用超异构设计，多了许多放大级，去掉了正反馈并使其工作更稳定。

<font color="#ff8000"> 再生电路Regenerative circuit</font>于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>，用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈，可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此，一个信号可以在一个阶段被放大20000甚至100000倍，而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定，开始振荡。无线电操作员必须不断地调整反馈量，以获得良好的接收效果。而现代无线电接收机采用超异构设计，多了许多放大级，去掉了正反馈并使其工作更稳定。

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。这降低了放大器的信号增益，但改善了它的线性度、输入阻抗、输出阻抗和带宽，并稳定了包括闭环增益等参数。同时，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，因为反馈元件一般随着制造公差、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。对于需要使用负反馈放大器的设计者来说，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，前板（用户界面）的变化，甚至是由于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。这降低了放大器的信号增益，但改善了它的线性度、输入阻抗、输出阻抗和带宽，并稳定了包括闭环增益等参数。同时，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，因为反馈元件一般不随着制造公差、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：如果信号反馈失相，则反馈为负，如果相位一致，则反馈为正。对于需要使用负反馈放大器的设计者来说，引入负反馈放大器的问题是，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（通常通过低通滤波来做到这一点）。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，前板（用户界面）的变化，甚至是由于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.

放大器可能会以示波器很难检测到的方式轻轻振荡，或者振荡可能非常大，只有非常扭曲或根本没有真正的信号，或者振荡会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似，因此被称为 "汽艇"。

放大器可能会以示波器很难检测到的方式轻轻振荡，有时的振荡也可能非常大，只有非常扭曲或根本没有真正的信号，甚至振荡也会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似，因此低频寄生振荡也被称为 "汽艇"。

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.|链接=Special:FilePath/Technics_SL-1210MK2.jpg]]

[[File:Technics SL-1210MK2.jpg|thumb|left|A phonograph turntable is prone to acoustic feedback.|链接=Special:FilePath/Technics_SL-1210MK2.jpg]]

Feedback is almost always considered undesirable when it occurs with a singer's or public speaker's microphone at an event using a sound reinforcement system or PA system. Audio engineers use various electronic devices, such as equalizers and, since the 1990s, automatic feedback detection devices to prevent these unwanted squeals or screeching sounds, which detract from the audience's enjoyment of the event. On the other hand, since the 1960s, electric guitar players in rock music bands using loud guitar amplifiers and distortion effects have intentionally created guitar feedback to create a desirable musical effect.  "I Feel Fine" by the Beatles marks one of the earliest examples of the use of feedback as a recording effect in popular music. It starts with a single, percussive feedback note produced by plucking the A string on Lennon's guitar. Artists such as the Kinks and the Who had already used feedback live, but Lennon remained proud of the fact that the Beatles were perhaps the first group to deliberately put it on vinyl. In one of his last interviews, he said, "I defy anybody to find a record—unless it's some old blues record in 1922—that uses feedback that way."

Feedback is almost always considered undesirable when it occurs with a singer's or public speaker's microphone at an event using a sound reinforcement system or PA system. Audio engineers use various electronic devices, such as equalizers and, since the 1990s, automatic feedback detection devices to prevent these unwanted squeals or screeching sounds, which detract from the audience's enjoyment of the event. On the other hand, since the 1960s, electric guitar players in rock music bands using loud guitar amplifiers and distortion effects have intentionally created guitar feedback to create a desirable musical effect.  "I Feel Fine" by the Beatles marks one of the earliest examples of the use of feedback as a recording effect in popular music. It starts with a single, percussive feedback note produced by plucking the A string on Lennon's guitar. Artists such as the Kinks and the Who had already used feedback live, but Lennon remained proud of the fact that the Beatles were perhaps the first group to deliberately put it on vinyl. In one of his last interviews, he said, "I defy anybody to find a record—unless it's some old blues record in 1922—that uses feedback that way."

在歌手或公众演讲者使用扩声系统或扩音系统的活动中，麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来，音频工程师使用各种电子设备，如均衡器或者自动反馈检测设备，来防止这些不受欢迎的尖叫声或尖叫声，这些声音影响了观众对活动的享受。另一方面，自20世纪60年代以来，摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果，有意制造吉他中的正反馈，以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。像 Kinks 和 Who 等艺术家已经在现场使用了正反馈，但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中，他说，“我敢说任何人都找不到这样的唱片，除非是1922年用这种方式录制的老蓝调唱片。”

在歌手或公众演讲者使用扩声系统或扩音系统的活动中，麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来，音频工程师使用各种电子设备，如均衡器或者自动反馈检测设备，来防止这些不受欢迎的尖叫声或尖叫声，这些声音影响了观众对活动的享受。另一方面，自20世纪60年代以来，摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果，有意制造吉他中的正反馈，以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。虽然像 Kinks 和 Who 等艺术家已经在表演中使用了正反馈，但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中，他说，“我敢说任何人都找不到这样的唱片，除非是1922年这张用这种方式录制的老蓝调唱片。”

Positive feedback is the amplification of a body's response to a stimulus. For example, in childbirth, when the head of the fetus pushes up against the cervix (1) it stimulates a nerve impulse from the cervix to the brain (2). When the brain is notified, it signals the pituitary gland to release a hormone called oxytocin(3). Oxytocin is then carried via the bloodstream to the uterus(4) causing contractions, pushing the fetus towards the cervix eventually inducing childbirth.

Positive feedback is the amplification of a body's response to a stimulus. For example, in childbirth, when the head of the fetus pushes up against the cervix (1) it stimulates a nerve impulse from the cervix to the brain (2). When the brain is notified, it signals the pituitary gland to release a hormone called oxytocin(3). Oxytocin is then carried via the bloodstream to the uterus(4) causing contractions, pushing the fetus towards the cervix eventually inducing childbirth.

生物学中的正反馈是指身体对刺激的反应的放大。例如，在分娩过程中，当胎儿的头顶到子宫颈时(1)，会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后，会向脑垂体发出信号，释放一种叫做催产素的激素(3)。催产素随后通过血液流向子宫(4)，引起宫缩，将胎儿推向子宫颈，最终促使分娩。

生物学中的正反馈是指身体对刺激的反应的放大。例如，在分娩过程中，当胎儿的头顶到子宫颈时(1)，会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后，会向脑垂体发出信号，释放一种叫做<font color="#ff8000"> 催产素oxytocin</font>的激素(3)。催产素随后通过血液流向子宫(4)，引起宫缩，将胎儿推向子宫颈，最终促使分娩。

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。<ref name=Hasty2002/>

正反馈是基因调控中研究较好的一种现象，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结果。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。<ref name=Christoph2001/>

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结果。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。<ref name=Christoph2001/>

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斯特模型（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)与周期性和随机性的动态干扰而产生的。

研究表明，在<font color="#32CD32"> 显生宙 </font>，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斯特模型（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)与周期性和随机性的动态干扰而产生的。

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.

Winner（1996）将有天赋的孩子描述为受到正反馈循环的驱动，这些反馈循环体现在他们自己的课程学习上，通过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 "狂热的掌握"。 Vandervert(2009a，2009b)提出，神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释，工作记忆中的思维/表现输出被反馈到小脑，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/>  

Winner（1996）将有天赋的孩子描述为受到正反馈循环的驱动，这些反馈循环体现在他们自己的课程学习上，通过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。<ref name=Winner1996/>Winner将这种正反馈循环称为 "狂热的掌握"。 Vandervert(2009a，2009b)提出，神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释，工作记忆中的思维/表现输出被反馈到小脑，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 ===