Introduction to Chaotic Dynamical Systems
Introduction to Chaotic Dynamical Systems
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DOI：
10.4324/9780429502309
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发表时间：
1992-12
期刊：
影响因子：
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通讯作者：
M. Bernhard
中科院分区：
文献类型：
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作者：
M. Bernhard
摘要：混沌理论是一门新兴学科，具有广泛的应用领域（如经济学、生物学、气象学等）。尽管如此，对于“混沌”还没有一个普遍接受的定义，因为它适用于一般的动力系统。各种方法的范围从定性描述的拓扑方法；到遍历理论中随机性、信息和熵的物理概念；发展用于获取定量信息的计算定义和算法。本文发展了混沌的一些现有定义，并讨论了混沌的几种定量度量。它旨在激发本科生和研究生的兴趣，并且适合具有高等微积分和常微分方程知识的人。在涵盖连续系统的混沌时，它可以作为Philip Beaver所做的工作的补充，该工作详细介绍了离散系统的混沌动力学。
Abstract : The emerging discipline known as "chaos theory" is a relatively new field of study with a diverse range of applications (i.e., economics, biology, meteorology, etc.). Despite this, there is not as yet a universally accepted definition for "chaos" as it applies to general dynamical systems. Various approaches range from topological methods of a qualitative description; to physical notions of randomness, information, and entropy in ergodic theory; to the development of computational definitions and algorithms designed to obtain quantitative information. This thesis develops some of the current definitions and discusses several quantitative measures of chaos. It is intended to stimulate the interest of undergraduate and graduate students and is accessible to those with a knowledge of advanced calculus and ordinary differential equations. In covering chaos for continuous systems, it serves as a complement to the work done by Philip Beaver, which details chaotic dynamics for discrete systems.