摘要
针对分数阶非线性系统普遍具有混沌特性的问题,采用观测系统吸引子相图、计算功率谱密度和最大Lyapunov指数等方法,分别分析了当参数固定(a=1)和变化时,分数阶统一系统随微分算子阶数变化时的动力学特性,得出了分数阶统一系统随系统参数和系统阶数变化而出现混沌状态的规律,研究了分数阶系统通向混沌的道路.研究表明:分数阶统一系统的动力学状态既与系统参数有关,又与系统的分数阶大小有关;在参数固定或参数变化时,分数阶统一系统均随阶数变化而分段呈现混沌状态;当微分算子阶数为0.3时,分数阶统一系统随参数变化经短暂混沌和边界转折点分叉而进入混沌.由此可见,分数阶统一系统具有丰富的动力学特性.
In order to investigate the chaos generally existing in nonlinear fractional-order systems, the dynamic characteristics of the fractional-order unified system varying with the differential operator orders respectively with fixed （ a = 1 ） and variable parameter are analyzed by observing the phase diagrams of system attractors and by calculating the power spectral density and the maximum Lyapunov exponent. The rules of chaos occurrence in the fractional-order unified system varying with the system parameter and the fractional order are then obtained, Moreover, the routs to chaos in the fractional order unified system are studied. The results show that （ 1 ） the dynamic states of the fractional-order unified system are related to both the system parameter and the fractional order; （2） the fractional-order unified systems with fixed and variable parameter are all piecewise chaotic at different fractional orders ; and （3） with the variation of system parameter at a differential operator order of 0.3, the fractional-order unified system enters into chaotic state by transient chaos and boundary crisis bifurcation. It is thus concluded that the fractional-order unified system is of complex dynamic characteristics.
出处
《华南理工大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2008年第8期6-10,共5页
Journal of South China University of Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(60672041)
中国博士后基金项目(20070420774)
关键词
分数阶系统
统一混沌系统
混沌
动力学特性
fractional-order system
unified chaotic system
chaos
dynamic characteristic
