分数阶自治动力学系统初值问题的递推公式及其应用  

Recurrence formula for initial value problems of fractional-order autonomous dynamics system and its application

作　　者：符五久 周林[1] 邓建杰 游泳[1] FU Wujiu;ZHOU Lin;DENG Jianjie;YOU Yong(School of Applied Science and Civil Engineering,Beijing Institute of Technology,Zhuhai,Zhuhai Guangdong 519088,China)

机构地区：[1]北京理工大学(珠海)数理与土木工程学院,广东珠海519088

出　　处：《计算机应用》2025年第2期556-562,共7页journal of Computer Applications

摘　　要：对分数阶微分动力学系统进行数值计算时,直接离散微分方程存在长时程储存困难。为解决这一问题,首先,将微分方程做一次积分,然后再离散化;同时,给出一个递推公式,并讨论它的适用条件。用该递推公式计算一些常见的非线性问题所得的结果都与其他数值方法的结果一致。由于二维分数阶连续动力学系统是否有混沌运动尚未有定论,应用这个递推公式对二维连续耦合Logistic模型进行研究,发现该系统仅由平衡点通过Hopf分岔产生极限环,不存在混沌运动。最后,给出分数阶二维连续Logistic系统运动的李雅普诺夫指数判据。When calculating fractional-order differential dynamics systems numerically,there are difficulties of longtime memory storage by discretizing differential equation directly.In order to solve this problem,firstly,the differential equation was integrated once and then discretized.At the same time,a recurrence formula was given and its applicable conditions were discussed.Some common non-linear problems were calculated by this formula.The results of the above were consistent with those of other numerical methods.As whether there is chaotic motion in two-dimensional fraction-order continuous dynamics system is not concluded,this recurrence formula was used to study the two-dimensional continuous coupled Logistic model.It is found that there is only the limit cycle generated by the equilibrium point through Hopf bifurcation in this system without chaotic motion.Finally,the Lyapunov exponent criterion for the motion of two-dimensional fractional-order continuous Logistic system was given.

关 键 词：分数阶 自治动力学系统 初值问题 递推公式 二维连续Logistic系统 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术] TP301.5[自动化与计算机技术—计算机科学与技术]