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第90行：
第90行： − + − + 第102行：
第102行： − 动力系统的概念是一个数学形式化的任何固定的“规则” ，描述了一个点的位置在其环境空间的时间依赖性。这些例子包括描述钟摆摆动的数学模型、管道中的水流量以及每年春天湖中鱼的数量。+ 第110行：
第110行： − 动力系统的状态是由一组实数决定的，或者更广泛地说是由适当的状态空间中的一组点决定的。系统状态的微小变化对应于数字的微小变化。这些数字也是几何空间ーー流形ーー的坐标。动力系统的演变规则是一个固定的规则，描述了当前状态下的未来状态。该规则可以是确定性的(在给定的时间间隔内，只有一个未来状态从当前状态跟随)或随机性的(状态的演变受到随机冲击)。+ − + 第120行：
第120行： − 动态主义又称动态假设或认知科学或动态认知中的动态假设，是以哲学家蒂姆 · 范 · 格尔德的著作为代表的认知科学的一种新方法。认为微分方程比传统的计算机模型更适合于建立认知模型。+ − + 第132行：
第132行： − 在数学中，非线性是一个不是线性的系统ーー也就是说，一个不满足叠加原理的系统。从技术上讲，非线性是任何需要求解的变量不能被写成独立分量的线性和的问题。非齐次系统除了自变量函数的存在外是线性的，根据严格的定义是非线性的，但这类系统通常与线性系统一起研究，因为只要知道特定的解，它们就可以转化为线性系统。+ − −
→Concepts： 第一遍翻译并表明疑问之处
优秀的数学动力系统理论包括，，，和。
优秀的数学动力系统理论包括，，，和。
== Concepts ==
== Concepts 概念==
=== Dynamical systems ===
=== Dynamical systems 动力系统===
{{main|Dynamical system (definition)}}
{{main|Dynamical system (definition)}}
The dynamical system concept is a mathematical formalization for any fixed "rule" that describes the time dependence of a point's position in its ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each spring in a lake.
The dynamical system concept is a mathematical formalization for any fixed "rule" that describes the time dependence of a point's position in its ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each spring in a lake.
动力系统是一个对任何描述了点的位置在周围环境随时间变化的“固定”规则的数学形式化。举例来说，描述钟摆摆动、管道中的水流以及每年春天湖中鱼的数量的数学模型都是属于动力系统的概念范畴。
A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space. Small changes in the state of the system correspond to small changes in the numbers. The numbers are also the coordinates of a geometrical space—a manifold. The evolution rule of the dynamical system is a fixed rule that describes what future states follow from the current state. The rule may be deterministic (for a given time interval only one future state follows from the current state) or stochastic (the evolution of the state is subject to random shocks).
A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space. Small changes in the state of the system correspond to small changes in the numbers. The numbers are also the coordinates of a geometrical space—a manifold. The evolution rule of the dynamical system is a fixed rule that describes what future states follow from the current state. The rule may be deterministic (for a given time interval only one future state follows from the current state) or stochastic (the evolution of the state is subject to random shocks).
动力系统的状态是由一组实数决定的，更广泛地说，是由适当的状态空间中的一组点决定的。系统状态的微小变化对应于数字的变化。这些数字也是几何空间——流形——的坐标。动力系统的演化是一个描述了在当前状态之后出现的未来状态的固定规则。这个规则可以是确定性的(在给定的时间间隔内，有且仅有一个未来状态在当前状态之后出现)，或随机性的(状态的演化受到随机因素的影响)。
=== Dynamicism ===
=== Dynamicism 动态主义===
[[Dynamicism]], also termed the ''dynamic hypothesis'' or the ''dynamic hypothesis in cognitive science'' or ''dynamic cognition'', is a new approach in [[cognitive science]] exemplified by the work of philosopher [[Tim van Gelder]]. It argues that [[differential equations]] are more suited to modelling [[cognition]] than more traditional [[computer]] models.
[[Dynamicism]], also termed the ''dynamic hypothesis'' or the ''dynamic hypothesis in cognitive science'' or ''dynamic cognition'', is a new approach in [[cognitive science]] exemplified by the work of philosopher [[Tim van Gelder]]. It argues that [[differential equations]] are more suited to modelling [[cognition]] than more traditional [[computer]] models.
Dynamicism, also termed the dynamic hypothesis or the dynamic hypothesis in cognitive science or dynamic cognition, is a new approach in cognitive science exemplified by the work of philosopher Tim van Gelder. It argues that differential equations are more suited to modelling cognition than more traditional computer models.
Dynamicism, also termed the dynamic hypothesis or the dynamic hypothesis in cognitive science or dynamic cognition, is a new approach in cognitive science exemplified by the work of philosopher Tim van Gelder. It argues that differential equations are more suited to modelling cognition than more traditional computer models.
动态主义，又称动态假设，或称认知科学、动态认知中的动态假设，是以哲学家Tim van Gelder的著作为代表的认知科学的一种新取向。动态主义认为微分方程比传统的计算机模型更适合于建立认知模型。
=== Nonlinear system ===
=== Nonlinear system 非线性系统===
{{main|Nonlinear system}}
{{main|Nonlinear system}}
In mathematics, a nonlinear system is a system that is not linear—i.e., a system that does not satisfy the superposition principle. Less technically, a nonlinear system is any problem where the variable(s) to solve for cannot be written as a linear sum of independent components. A nonhomogeneous system, which is linear apart from the presence of a function of the independent variables, is nonlinear according to a strict definition, but such systems are usually studied alongside linear systems, because they can be transformed to a linear system as long as a particular solution is known.
In mathematics, a nonlinear system is a system that is not linear—i.e., a system that does not satisfy the superposition principle. Less technically, a nonlinear system is any problem where the variable(s) to solve for cannot be written as a linear sum of independent components. A nonhomogeneous system, which is linear apart from the presence of a function of the independent variables, is nonlinear according to a strict definition, but such systems are usually studied alongside linear systems, because they can be transformed to a linear system as long as a particular solution is known.
在数学中，非线性系统是指系统不是线性的——也就是说，一个不满足叠加原理的系统。更通俗地说，非线性系统是需要求解的变量不能被写成它的独立分量的线性和的系统。非齐次系统根据定义严格来说是非线性的，但是它的自变量函数是线性的 --[[用户:嘉树|嘉树]]（[[用户讨论:嘉树|讨论]]）+讨论如何翻译本句 。非齐次系统通常与线性系统一起研究，因为只要知道特解，它们就可以转化为线性系统。
== Related fields ==
== Related fields ==