显含时滞分数阶动力学系统的混沌特性及同步研究

项目名称： 显含时滞分数阶动力学系统的混沌特性及同步研究

项目编号： No.60873200

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 周尚波

作者单位： 重庆大学

项目金额： 20万元

中文摘要： 本项目拟研究显含分数阶微分动力系统的混沌特性、同步及其计算机仿真问题，构造该类混沌系统的控制与同步系统，并研究其稳定性和收敛性问题。我们将从分数阶的神经网络模型（CNN或HNN模型）出发，重点对带显含时滞（包括离散和连续时滞）的分数阶系统进行研究。主要研究内容是：（1）分数阶系统的动力学行为。包括稳定性、分岔和混沌现象。稳定性主要是渐近稳定和指数稳定性, 混沌特征及分析主要是研究其Lyapunov指数的估算方法；（2）分数阶混沌系统的控制与同步。利用稳定性的研究成果，构造和研究混沌控制系统和两个混沌系统之间的同步问题；（3）分数阶系统的数值仿真实验。本项目将研究带显含时滞的分数阶系统的数值仿真问题；（4）对分数阶混沌在密码学中的应用作初步探索。本项目的研究意义在于丰富分数阶微分动力系统的理论，为混沌在保密通信等领域的应用提供新思路。

中文关键词： 分数阶导数;时滞;混沌;同步

英文摘要： In this project, the chaotic characteristics, synchronization and computer simulation of the fractional differentiable dynamical systems will be studied; the control and synchronization systems of the chaotic systems will be constructed; their stability and convergence will also be researched. We will maily research the fractional systems with explicit time delay (include discreted and continuous delays) from the fractional neural network model(CNN or HNN models). The main contents include: (1) The dynamic behaviors of the fractional systems, including stability, bifurcation and chaotic phenomenon. The stability maily refers to the asymptotical stability and exponential stability. Chaotic characteristics and their analysis concentrate on the estimating method of the Lyapunov exponents. (2) Control and synchronization of the fractional chaotic systems. The results of the stability are applied to construct and study the chaotic control systems and the synchronization of two chaotic systems. (3) Numerical simulation experiments of the fractional systems. Numerical simulations of the fractional systems will be reaearched in this project. (4) A primary research on the application of the fractional chaos in cryptography will be made. The research significance of this project focuses on enriching the theory of the fractional differentiable dynamical systems, and providing new ideas for the application of chaos in the fileds such as secure communication.

英文关键词： fractional derivative; time delay; chaos; synchronization