分数阶二维线性系统的奇点类型及其邻域内的轨道性态  

Classification of the singular point and behavior of orbits in neighborhood of the singular point for the fractional 2-dimensional linear system

作　　者：罗静 冀小明[2] LUO Jing;JI Xiao-ming(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China;School of Preparatory Education,Southwest Minzu University,Chengdu 610041,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]西南民族大学预科教育学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2022年第2期207-215,共9页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金项目(11361023);重庆市科委项目(cstc2018jcyjAX0766)。

摘　　要：分数阶动力系统在众多自然科学和工程领域中有很好的应用,但由于太过复杂,分数阶动力系统至今没有得到较为系统和全面的研究.借助于一系列的线性变换和Laplace变换,利用Mittag-Leffler函数的敛散性质,首次较为系统地研究了分数阶二维线性系统的奇点分类情况,进一步分析了各种奇点邻域内轨道的动力学性态,最终给出了系统在奇点邻域内轨线分布的平面图貌.研究还发现,分数阶二维线性系统没有中心型奇点,也不存在闭轨道和相应的周期解,这为分数阶驻定微分方程组不存在周期解提供了有力的佐证.Fractional dynamical system has been used in many natural science and engineering fields,and fractional dynamical system has not been studied systematically and comprehensively because of its complexity.With the help of a series of linear and Laplace transformations,the classification of singular point of the fractional two-dimensional linear system was studied systematically for the first time by using the convergence and divergence properties of Mittag-Leffler functions.The dynamical behavior of the orbits in the neighborhood of singular point was further analyzed,and the planar diagram of the distribution of the orbits in the neighborhood of singular point was given.It was also found that there were no central point,closed orbits and corresponding periodic solutions in fractional-order two-dimensional linear systems,which provides a strong evidence for the absence of periodic solutions in fractional order stationary differential equations.

关 键 词：分数阶动力系统 LAPLACE变换 奇点类型的判定 动力学性态 平面图相 

分 类 号：O175[理学—数学]