论文标题
Lyapunov指数与对混沌系统参数的敏感依赖之间的联系
A connection between Lyapunov exponents and sensitive dependence on parameters of chaotic systems
论文作者
论文摘要
混乱对参数的敏感依赖性在研究动态系统的整合性和稳定性方面引起了极大的兴趣。先前的工作提出了通过拓扑标准或大型数值模拟来确定对参数的敏感依赖性的方法。在本文中，我们表明，当系统的Lyapunov指数随参数的变化而变化时，系统在与所考虑的参数相关的轨道中呈指数分数。我们使用此结果在不确定性间隔中探索对参数的敏感依赖性，并得出结论，该现象的表征与我们确定系统的Lyapunov指数的能力直接相关。
The sensitive dependence of chaos on parameters is a topic of great interest in the study of integrability and stability of dynamical systems. Previous work has proposed ways to identify the sensitive dependence on parameters by topological criteria or large numerical simulations. In this paper, we show that when the Lyapunov exponents of the system vary with a change in the parameters, the system diverges exponentially in the orbits associated with the considered parameters. We use this result to explore the sensitive dependence on parameters in an uncertainty interval and conclude that the characterization of this phenomenon is directly related to our ability to determine the Lyapunov exponents of the system for different parameters.
