Caputo型分数阶三维自治系统在相空间中的动力学行为  

Dynamic behavior in phase space of the Caputo fractional autonomous systems of 3-dimension

作　　者：张宏杰 芮伟国 ZHANG Hong-jie;RUI Wei-guo(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《云南大学学报（自然科学版）》2021年第5期849-858,共10页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11361023);重庆市科委基础研究与前沿探索专项项目(cstc2018jcyjAX0766).

摘　　要：通过一系列的非奇异的线性变换和Laplace变换,并借助于特殊函数Mittag-Leffler函数的敛散性,首次较为全面和深入地研究了Caputo型分数阶三维自治系统在相空间中的各种动力学行为,并进一步分析了系统在相空间内的平衡点随参数变化的情况以及平衡点邻域内轨线的动力学性态,最终较为全面地给出了该系统关于轨线分布的空间图貌.研究结果显示,Caputo型分数阶三维动力系统既不存在中心型的平衡点,也不存在闭轨道,从而不存在相应的周期解,这为分数阶线性微分方程组不存在周期解提供了一个新的例证.Through a series of non-singular linear transformation and Laplace transformation,and with help of properties of the convergence and divergence of special function Mittag-Leffler function,the dynamic behavior of Caputo type fractional-order autonomous system of three-dimension in phase space were studied comprehensively and deeply for the first time.The variation cases of equilibrium points with parameters and the dynamic behaviors of line in the neighborhood of equilibrium points in phase space were further analyzed.Finally,the graphic maps of the orbit distribution of the system were given overall.The research results show that there is neither a central equilibrium point nor a closed orbit in the Caputo type fractional-order three-dimensional dynamic system,thus there is no corresponding periodic solution,which provides a new example for the fractional-order linear differential equations without periodic solution.

关 键 词：分数阶动力系统 非奇异的线性变换和Laplace变换 Mittag-Leffler函数 相空间 轨线的动力学性态 

分 类 号：O175.08[理学—数学]