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This theory deals with the long-term qualitative behavior of dynamical systems, and studies the nature of, and when possible the solutions of, the equations of motion of systems that are often primarily mechanical or otherwise physical in nature, such as planetary orbits and the behaviour of electronic circuits, as well as systems that arise in biology, economics, and elsewhere. Much of modern research is focused on the study of chaotic systems.
This theory deals with the long-term qualitative behavior of dynamical systems, and studies the nature of, and when possible the solutions of, the equations of motion of systems that are often primarily mechanical or otherwise physical in nature, such as planetary orbits and the behaviour of electronic circuits, as well as systems that arise in biology, economics, and elsewhere. Much of modern research is focused on the study of chaotic systems.
这个理论处理动力系统的长期定性行为。<font color="red">如果能够得到解的话，还可以研究系统的运动方程。这些方程通常运用到机械或物理研究领域，如行星轨道和电子电路，以及出现在生物学，经济学和其他地方的系统。</font>现代的研究大多集中在对混沌系统的研究上。
<font color="blue">这个理论处理动力系统的长周期性的行为，并且研究系统的动力方程的规律，努力求得可能的解。这些系统通常是一些自然领域里的机械系统或其他物理系统，例如行星轨道和电子电路，也包括一些生物学、经济学和其他学科里的系统。现代的研究大多集中在对混沌系统的研究上。</font>
这个理论处理动力系统的长期定性行为，<font color="blue">并且研究系统的动力方程的规律，努力求得可能的解。这些系统通常是一些自然领域里的机械系统或其他物理系统，例如行星轨道和电子电路，也包括一些生物学、经济学和其他学科里的系统。</font>现代的研究大多集中在对混沌系统的研究上。
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems. Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does the long-term behavior of the system depend on its initial condition?"
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems. Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does the long-term behavior of the system depend on its initial condition?"
动力系统理论和'''混沌理论 Chaos Theory'''是用来处理动力系统的<font color="red">长期定性行为</font><font color="blue"> 长周期性行为</font>的理论。寻找动力系统方程的精确解通常是很难达到的。<font color="blue"> 因此，</font>这两个理论的重点不在于找到精确解，而是回答如下的问题，如“系统长期来看是否会稳定下来，如果可以，那么可能的稳定状态是什么样的?”，或“系统长期的行为是否取决于其初始条件?”
动力系统理论和'''混沌理论 Chaos Theory'''是用来处理动力系统的长期定性行为的理论。寻找动力系统方程的精确解通常是很难达到的。这两个理论的重点不在于找到精确解，而是回答如下的问题，如“系统长期来看是否会稳定下来，如果可以，那么可能的稳定状态是什么样的?”，或“系统长期的行为是否取决于其初始条件?”