非线性分数阶系统的混沌特性研究

项目名称： 非线性分数阶系统的混沌特性研究

项目编号： No.11202148

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 贾红艳

作者单位： 天津科技大学

项目金额： 25万元

中文摘要： 近年来，混沌理论与应用均得到了快速发展，同时，也出现了一些新问题需要进一步研究。其中之一就是关于非线性分数阶混沌系统的研究。由于分数阶混沌理论及应用的研究刚刚起步，所以有大量的工作需要深入去做。目前，关于分数阶混沌系统的研究大多只是处于初步的仿真研究阶段，本项目将对分数阶系统在分形分析、混沌拓扑马蹄分析、电路实现等几个方面进行深入研究。本项目的创新性及研究意义在于：（1）对非线性分数阶系统进行深入分析，说明其混沌特性，为混沌应用提供好的模型；（2）采用拓扑马蹄引理，借助计算机辅助证明，证明在分数阶混沌系统中存在着拓扑马蹄，进而说明其混沌特性,从理论上验证非线性分数阶系统的混沌存在性；（3）通过模拟电路实现分数阶混沌系统，从物理意义上说明其混沌特性，为分数阶混沌应用提供技术准备。总之，本项目的研究工作将为今后分数阶混沌理论研究及应用提供理论基础和技术支持。

中文关键词： 分数阶；混沌；拓扑马蹄；同步控制；模拟电路实现

英文摘要： In recent years, great progress has been achieved for the theory and application of chaos. At the same time, there appear are some new questions which need further research. One of them is the study of nonlinear fractional chaotic system. As the research for fractional chaotic system has just started, there is a lot of work to be done in depth. At the present time, the study on the fractional chaotic system are just simulation analysis, this project is mainly to solve the following questions, such as bifurcation analysis for fractional chaotic systems, topological horseshoe analysis for fractional chaotic systems, circuit implementation for fractional chaotic systems, and etc. The innovation work and research significance is summarized as follows.(1) analyzes the nonlinear fractional chaotic systems in detail,show their chaotic characteristics，and provide a better model for the application of chaos.(2) by use of topological horseshoe lemma and the computer-assisted proof, verify that topological horseshoes exist in fractional chaotic systems, show the chaotic characteristic of fractional chaotic systems, and thus the existence of chaos is proved theoretically.(3) by using analog circuits, implement fractional chaotic systems, prove the chaotic existence in fractional systems physically, and provide technical pre

英文关键词： fractional-order；chaos；topological horseshoe；synchronization control；analog circuit implementation