一类离散时滞系统的复杂动力学行为研究

Complex Dynamic Behaviors Research for Class of Discrete Systems with Time-Delay

在混沌巨大潜在应用前景的推动下,混沌控制已经引起了学者们越来越浓厚的研究兴趣。混沌的一些特征参量为系统是否呈现混沌行为提供了直接的判断依据。针对一类离散时滞系统,研究系统动力学行为随时滞参数变化的情况。在得到系统有界的前提下,分析一类基于传染病传播机理的复杂网络模型,研究传染病的传播动力学行为随最大李雅普诺夫指数变化的情况。基于Wolf重构法,仿真出系统最大李雅普诺夫指数随着时滞参数变化的曲线图。当最大李雅普诺夫指数大于零,系统呈现混沌行为,传染病在有界区域内传播;反之,系统收敛,传染病则会慢慢的消失。

Spurred by the great potential in applications, the control of chaos has attracted increasing attentions in recent years. Some very desirable features of chaos in these applications have provided direct judgments that the sys- tem is chaotic or not. In this paper, for a class of discrete time - delayed systems, the dynamic behaviors were stud- ied as the time - delayed parameter changes. As a precondition that the boundedness of systems is obtained, a class of complex networks based on the infectious diseases were studied, and the spreading dynamical behaviors about the largest Lyapunov exponent were discussed in detail. Based on the method of Wolf reconstruction, the picture of the largest Lyapunov exponent about the time - delayed parameter was figured out, and a conclusion was derived. When the largest Laypunov exponent is positive, the systems are chaos, and the infectious disease will spread in a bounded area. Otherwise, the systems are convergent, and the infectious disease will vanish slowly~