分数阶系统的脉冲混沌动力学及稳定性

项目名称： 分数阶系统的脉冲混沌动力学及稳定性

项目编号： No.11202249

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： 李东

作者单位： 重庆大学

项目金额： 24万元

中文摘要： 实际系统通常大都是分数阶的，脉冲是事物在其发展过程中受到瞬时扰动而产生的一种普遍现象，目前对具有脉冲的分数阶系统的研究尚处于萌芽阶段。针对其基础性理论的严重不足，本项目拟结合分数阶系统和脉冲系统的研究，探索脉冲分数阶系统的建模、混沌行为、稳定性和同步等动力学问题的研究方法。主要研究内容有：(1)建立具有脉冲机制和分数阶系统特征的系统模型，并采用Topological horseshoe方法，提出适合于脉冲分数阶系统的混沌分析的理论判定依据；(2)针对脉冲分数阶系统的特点，利用分段Lyapunov方法，研究脉冲分数阶系统的稳定性；(3)利用稳定性分析结果，采用自适应等控制方法，提出同结构和异结构的脉冲分数阶系统同步理论。本课题所研究的成果将为复杂动力系统较为精确的刻画和研究提供切实有效的、先进的技术手段，解决以前只能用脉冲整数阶系统进行近似描述的瓶颈问题，有着重要的理论意义和应用价值。

中文关键词： 分数阶系统；混沌；稳定性；同步；Lyapunov函数

英文摘要： Fractional calculus deals with derivatives and integrations of arbitrary order and has found many applications in many fields. Impulse is universal phenomenon in some system due to the instant disturb. But the study of fractional order with impulse is far few. For the severe shortage of basic theory of impulsive differential equation, the study method of modeling dynamics such as chaotic behavior, stability and synchronization is explored by the study for impulsive system and fractional order system in the project. The main research content includes: (i) the model of fractional order system with impulse will be established, and the theory of chaos analysis of impulsive fractional order system will be discussed by the Topological horseshoe method. (ii) For the characteristic of impulsive fractional system. the stability of the impulsive fractional order system will be investigated by the piecewise Lyapunov function.(iii) Based on the results of stability analysis, the theory of synchronization in the isostructure and different structure impulsive fractional order system will be discussed by using the self-adapting method. If the predictive target is realized, the study results of the project will provide effective and advanced technology to precision modeling and studying a complex dynamic system. The bottle nec

英文关键词： Fractional order systems；Chaos；Stability；Synchronization；Lyapunov function