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在人类发展方面，动力系统理论已经被用来增强和简化 Erik Erikson 的'''社会心理发展8阶段理论 Eight Stages of Psychosocial Development'''，并提供了一个检验人类发展普遍模式的标准方法。该方法基于斐波那契数列的'''自组织性 self-organizing'''和'''分形 Fractal''' 特性。利用数学模型，人类发展的自然进程被分为8个生命阶段: 早期婴儿期(0-2岁)、幼儿期(2-4岁)、童年早期(4-7岁)、童年中期(7-11岁)、青春期(11-18岁)、成年早期(18-29岁)、成年中期(29-48岁)和老年成年期(48-78岁及以上)。

在人类发展方面，动力系统理论已经被用来增强和简化 Erik Erikson 的'''社会心理发展8阶段理论 Eight Stages of Psychosocial Development'''，并提供了一个检验人类发展普遍模式的标准方法。该方法基于斐波那契数列的'''自组织性 self-organizing'''和'''分形 Fractal''' 特性。利用数学模型，人类发展的自然进程被分为8个生命阶段: 早期婴儿期(0-2岁)、幼儿期(2-4岁)、童年早期(4-7岁)、童年中期(7-11岁)、青春期(11-18岁)、成年早期(18-29岁)、成年中期(29-48岁)和老年成年期(48-78岁及以上)。

 

According to this model, stage transitions between age intervals represent self-organization processes at multiple levels (e.g., molecules, genes, cell, organ, organ system, organism, behavior, and environment). For example, at the stage transition from [[adolescence]] to [[young adulthood]], and after reaching the critical point of 18 years of age (young adulthood), a peak in [[testosterone]] is observed in males<ref>{{cite journal |last1=Kelsey |first1=T. W. |title=A validated age-related normative model for male total testosterone shows increasing variance but no decline after age 40 years. |journal=PLOS One |volume=9 |issue=10 |pages=e109346 |doi=10.1371/journal.pone.0109346|pmid=25295520 |year=2014 |pmc=4190174 |bibcode=2014PLoSO...9j9346K }}</ref> and the period of optimal [[fertility]] begins in females.<ref>{{cite book |last1=Tulandi |first1=T. |title=Preservation of fertility |date=2004 |publisher=Taylor & Francis |pages=1–20}}</ref> Similarly, at age 30 optimal fertility begins to decline in females,<ref name="Social Science 2008">{{cite journal |last1=Blanchflower |first1=D. G. |title=Is well-being U-shaped over the life cycle? |journal=Social Science & Medicine |volume=66 |issue=8 |pages=1733–1749 |doi=10.1016/j.socscimed.2008.01.030|pmid=18316146 |year=2008 |citeseerx=10.1.1.63.5221 }}</ref> and at the stage transition from [[middle adulthood]] to older adulthood at 48 years, the average age of onset of [[menopause]] occurs.<ref name="Social Science 2008"/>

According to this model, stage transitions between age intervals represent self-organization processes at multiple levels (e.g., molecules, genes, cell, organ, organ system, organism, behavior, and environment). For example, at the stage transition from [[adolescence]] to [[young adulthood]], and after reaching the critical point of 18 years of age (young adulthood), a peak in [[testosterone]] is observed in males<ref>{{cite journal |last1=Kelsey |first1=T. W. |title=A validated age-related normative model for male total testosterone shows increasing variance but no decline after age 40 years. |journal=PLOS One |volume=9 |issue=10 |pages=e109346 |doi=10.1371/journal.pone.0109346|pmid=25295520 |year=2014 |pmc=4190174 |bibcode=2014PLoSO...9j9346K }}</ref> and the period of optimal [[fertility]] begins in females.<ref>{{cite book |last1=Tulandi |first1=T. |title=Preservation of fertility |date=2004 |publisher=Taylor & Francis |pages=1–20}}</ref> Similarly, at age 30 optimal fertility begins to decline in females,<ref name="Social Science 2008">{{cite journal |last1=Blanchflower |first1=D. G. |title=Is well-being U-shaped over the life cycle? |journal=Social Science & Medicine |volume=66 |issue=8 |pages=1733–1749 |doi=10.1016/j.socscimed.2008.01.030|pmid=18316146 |year=2008 |citeseerx=10.1.1.63.5221 }}</ref> and at the stage transition from [[middle adulthood]] to older adulthood at 48 years, the average age of onset of [[menopause]] occurs.<ref name="Social Science 2008"/>

In sports biomechanics, dynamical systems theory has emerged in the movement sciences as a viable framework for modeling athletic performance. From a dynamical systems perspective, the human movement system is a highly intricate network of co-dependent sub-systems (e.g. respiratory, circulatory, nervous, skeletomuscular, perceptual) that are composed of a large number of interacting components (e.g. blood cells, oxygen molecules, muscle tissue, metabolic enzymes, connective tissue and bone). In dynamical systems theory, movement patterns emerge through generic processes of self-organization found in physical and biological systems. There is no research validation of any of the claims associated to the conceptual application of this framework.

In sports biomechanics, dynamical systems theory has emerged in the movement sciences as a viable framework for modeling athletic performance. From a dynamical systems perspective, the human movement system is a highly intricate network of co-dependent sub-systems (e.g. respiratory, circulatory, nervous, skeletomuscular, perceptual) that are composed of a large number of interacting components (e.g. blood cells, oxygen molecules, muscle tissue, metabolic enzymes, connective tissue and bone). In dynamical systems theory, movement patterns emerge through generic processes of self-organization found in physical and biological systems. There is no research validation of any of the claims associated to the conceptual application of this framework.

在运动生物力学中，动力系统理论新兴地成为对运动表现建模的可行框架。从动力系统的角度来看，人类的运动系统是由高度复杂和相互依赖的子系统网络（如呼吸、循环、神经、骨骼肌系统和知觉系统等）组成的，它们由大量相互作用的部分组成（包括血细胞、氧分子、肌肉组织、代谢酶、结缔组织和骨骼等)。动力系统理论中，运动模式通过物理系统和生物系统中的一般自组织过程出现。没有任何研究证实与这一框架的概念相关的任何主张。

<font color='red'>在运动生物力学中，动力系统理论新兴地成为对运动表现建模的可行框架。</font><font color='blue'>在运动生物力学中，动力系统理论在运动科学中崭露头角，成为一种对运动表现建模的可行框架。</font>从动力系统的角度来看，人类的运动系统是由高度复杂和相互依赖的子系统网络（如呼吸、循环、神经、骨骼肌系统和知觉系统等）组成的，它们由大量相互作用的部分组成（包括血细胞、氧分子、肌肉组织、代谢酶、结缔组织和骨骼等)。动力系统理论中，运动模式通过物理系统和生物系统中的一般自组织过程出现。没有任何研究证实与这一框架的概念<font color='blue'>应用</font>相关的任何主张。

=== In cognitive science 在认知科学中的应用===

=== In cognitive science 在认知科学中的应用===

Dynamical system theory has been applied in the field of neuroscience and cognitive development, especially in the neo-Piagetian theories of cognitive development. It is the belief that cognitive development is best represented by physical theories rather than theories based on syntax and AI. It also believed that differential equations are the most appropriate tool for modeling human behavior. These equations are interpreted to represent an agent's cognitive trajectory through state space. In other words, dynamicists argue that psychology should be (or is) the description (via differential equations) of the cognitions and behaviors of an agent under certain environmental and internal pressures. The language of chaos theory is also frequently adopted.

Dynamical system theory has been applied in the field of neuroscience and cognitive development, especially in the neo-Piagetian theories of cognitive development. It is the belief that cognitive development is best represented by physical theories rather than theories based on syntax and AI. It also believed that differential equations are the most appropriate tool for modeling human behavior. These equations are interpreted to represent an agent's cognitive trajectory through state space. In other words, dynamicists argue that psychology should be (or is) the description (via differential equations) of the cognitions and behaviors of an agent under certain environmental and internal pressures. The language of chaos theory is also frequently adopted.

动力系统理论已经被应用于神经科学和认知发展领域，特别是在认知发展的'''新皮亚杰学派 neo-Piagetian'''中。人们相信，物理学理论比句法学理论和人工智能理论更能代表认知发展。人们还相信微分方程是人类行为建模最合适的工具。人们认为微分方程可以解释为通过状态空间代表一个主体的认知轨迹的算式。换句话说，动力学家认为心理学应该(或者是)(通过微分方程)描述在一定的环境和内部压力下的主体的认知和行为的学科。混沌理论在相关领域也经常被采用。

动力系统理论已经被应用于神经科学和认知发展领域，特别是在认知发展的'''新皮亚杰学派 neo-Piagetian'''中。人们相信，物理学理论比句法学理论和人工智能理论更能代表认知发展。人们还相信微分方程是人类行为建模最合适的工具。<s>人们认为</s>微分方程可以解释为通过状态空间代表一个主体的认知轨迹的算式。换句话说，动力学家认为心理学应该<font color='blue'>是</font>(或者<font color='blue'>就</font>是)(通过微分方程)描述在一定的环境和内部压力下的主体的认知和行为的学科。混沌理论在相关领域也经常被采用。

In it, the learner's mind reaches a state of disequilibrium where old patterns have broken down. This is the phase transition of cognitive development. Self-organization (the spontaneous creation of coherent forms) sets in as activity levels link to each other. Newly formed macroscopic and microscopic structures support each other, speeding up the process. These links form the structure of a new state of order in the mind through a process called scalloping (the repeated building up and collapsing of complex performance.) This new, novel state is progressive, discrete, idiosyncratic and unpredictable.

In it, the learner's mind reaches a state of disequilibrium where old patterns have broken down. This is the phase transition of cognitive development. Self-organization (the spontaneous creation of coherent forms) sets in as activity levels link to each other. Newly formed macroscopic and microscopic structures support each other, speeding up the process. These links form the structure of a new state of order in the mind through a process called scalloping (the repeated building up and collapsing of complex performance.) This new, novel state is progressive, discrete, idiosyncratic and unpredictable.

在学习的过程中，旧的模式被打破了，学习者的思维达到了一种不平衡的状态。这是认知发展的阶段性转变。自组织(连贯的自发创造(the spontaneous creation of coherent forms))在'''活动水平 Activity Levels'''相互联系时产生。新形成的宏观和微观结构相互支持，加速了这一过程。这些联系在头脑中形成了一种具有新状态的结构，这个过程被称为“扇贝化 Scalloping”，也就是头脑的复杂性能的不断累积和崩溃的过程 --[[用户:嘉树|嘉树]]（[[用户讨论:嘉树|扇贝化的翻译拿不准，这句话的描述比较抽象]]）。这种新的状态是渐进的、离散的、异质的的和不可预知的。

在学习的过程中，旧的模式被打破了，学习者的思维达到了一种不平衡的状态。这是认知发展的阶段性转变。自组织(连贯的自发创造(the spontaneous creation of coherent forms))在'''活动水平 Activity Levels'''相互联系时产生。新形成的宏观和微观结构相互支持，加速了这一过程。这些联系在头脑中形成了一种<font color='blue'>有序的<s>具有</s></font>新状态<s>的</s>结构，这个过程被称为“扇贝化 Scalloping”，也就是头脑的复杂<font color='red'>性能</font><font color='blue'>表现</font>的不断累积和崩溃的过程 --[[用户:嘉树|嘉树]]（[[用户讨论:嘉树|扇贝化的翻译拿不准，这句话的描述比较抽象]]）。这种新的状态是渐进的、离散的、异质的的和不可预知的。

The application of Dynamic Systems Theory to study second language acquisition is attributed to Diane Larsen-Freeman who published an article in 1997 in which she claimed that second language acquisition should be viewed as a developmental process which includes language attrition as well as language acquisition. In her article she claimed that language should be viewed as a dynamic system which is dynamic, complex, nonlinear, chaotic, unpredictable, sensitive to initial conditions, open, self-organizing, feedback sensitive, and adaptive.

The application of Dynamic Systems Theory to study second language acquisition is attributed to Diane Larsen-Freeman who published an article in 1997 in which she claimed that second language acquisition should be viewed as a developmental process which includes language attrition as well as language acquisition. In her article she claimed that language should be viewed as a dynamic system which is dynamic, complex, nonlinear, chaotic, unpredictable, sensitive to initial conditions, open, self-organizing, feedback sensitive, and adaptive.

动力系统理论在二语习得研究中的应用归功于 Diane Larsen-Freeman，她在1997年发表的一篇文章中认为，二语习得应该被看作是一个包括语言流失和习得在内的发展过程。她在文章中认为，语言应该被看作是一个动态的、复杂的、非线性的、混沌的、不可预知的、对初始条件敏感的、开放的、自组织的、反馈敏感的和适应性的动力系统。

动力系统理论在二语习得研究中的应用归功于 Diane Larsen-Freeman，她在1997年发表的一篇文章中认为，二语习得应该被看作是一个包括语言流失和<font color='blue'>语言</font>习得在内的发展过程。她在文章中认为，语言应该被看作是一个动态的、复杂的、非线性的、混沌的、不可预知的、对初始条件敏感的、开放的、自组织的、反馈敏感的和适应性的动力系统。

== See also 参见==

== See also 参见==

*[https://web.archive.org/web/20080613053119/http://www.cogs.indiana.edu/Publications/techreps2000/241/241.html Dynamic Systems 动力系统] Encyclopedia of Cognitive Science entry. --[[用户:嘉树|嘉树]]（[[用户讨论:嘉树|这是一个嵌套的链接，但好像只能鼠标点击并超链接到内嵌的那个]]）认知科学百科全书

*[https://web.archive.org/web/20080613053119/http://www.cogs.indiana.edu/Publications/techreps2000/241/241.html Dynamic Systems 动力系统] Encyclopedia of Cognitive Science entry. --[[用户:嘉树|嘉树]]（[[用户讨论:嘉树|这是一个嵌套的链接，但好像只能鼠标点击并超链接到内嵌的那个]]）认知科学百科全书

*[http://mathworld.wolfram.com/DynamicalSystem.html Definition of dynamical system 动力系统的定义] in MathWorld. 在MathWorld.wolfram.com储存的定义

*[http://mathworld.wolfram.com/DynamicalSystem.html Definition of dynamical system 动力系统的定义] in MathWorld. 在MathWorld.wolfram.com储存的定义