含参量分数阶微分系统的基本分岔分析  

ANALYSIS THE FUNDMENTAL BIFURCATIONS OF THE FRACTIONAL DIFFERENTIAL SYSTEMS WITH THE PARAMETERS

作　　者：钱德亮[1] 陈阳泉[2,3] 

机构地区：[1]中原工学院数学系,郑州450007 [2]加利福尼亚大学默赛德分校工程学院,机械电子,嵌入系统与自动化实验室,加利福尼亚953435200 [3]犹他州立大学电子与计算机工程系,犹他843224120

出　　处：《动力学与控制学报》2013年第3期211-220,共10页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(10872119);河南省自然科学基金(112300410022);中国博士后基金(2012M510885)~~

摘　　要：本文中,我们讨论了含参量分数阶微分系统的基本分岔,即跨临界分岔、折叠分岔与音叉分岔.首先,根据分数阶Lyapunov方法,讨论了含参量分数阶微分系统的稳定性,并给出了这些基本分岔的相图.其次,根据Taylor展式与隐函数定理,研究了分数阶微分系统的规范形,从而求出这些基本分岔的拓扑规范形.This paper investigates the fundmental bifurcations for the fractional differential systems involving one parameter in the variable space. Applying the Lyapunov direct method to the fractional differential systems to prove the stability or the instability of the equilibria, the phase portraits of the bifurcations are obtained. With the help of the Taylor＇ expansion and the Implicit Function Theorem in the classical sense, the normal forms of the bifurcations of the fractional differential systems are calculated. By using the topological equivalent map which depend on one parameter, the topological normal forms of the bifurcations of the fractional differential systems are derived.

关 键 词：分数阶微分系统 CAPUTO分数阶导数 折叠分岔 跨临界分岔 音叉分岔 

分 类 号：O175[理学—数学]