脉冲微分混沌系统动力学数值模拟与分析  

NUMERICAL SIMULATION AND ANALYSIS OF DYNAMICS OF IMPULSIVE DIFFERENTIAL CHAOTIC SYSTEM

作　　者：郭俊荣 严平 Guo Junrong;Yan Ping(College of Science,Zhejiang Agriculture and Forestry University,Hangzhou 311300,China;Department of Mathematics and Statistics,University of Helsinki,Helsinki 00014,Finland)

机构地区：[1]浙江农林大学理学院,杭州311300 [2]赫尔辛基大学数学与统计系,芬兰00014

出　　处：《数值计算与计算机应用》2022年第1期27-37,共11页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(41730638)资助.

摘　　要：由于脉冲微分混沌系统具有复杂的性态,在理论分析时具有一定的难度,而数值分析在一定程度上可以提供一些指导,所以数值模拟方法成为脉冲微分混沌系统研究的重要手段.该文设计了脉冲微分混沌系统的动力学分析算法,并将数值解以可视化的形式展现,绘制出方程组解的相图、分岔图、Poincare截面.以具有Holling type-Ⅱ功能反应函数的Gompertz病毒传染病模型为例验证算法的可行性,进行了数值模拟,得到了一些有意义的结论.Due to the complex behavior of impulsive differential systems,the theoretical analysis has certain difficulties,and numerical analysis provides some guidance to a certain extent,so the numerical simulation method has become an important means of impulsive differential equation research.This paper designs an algorithm for the dynamics analysis of impulsive differential equations,and the numerical solutions are visualized,and the phase diagrams,bifurcation diagrams,and Poincar ’e diagrams of the solutions of the system are drawn.Taking the Gompertz virus infectious disease model with Holling type-Ⅱ functional response function as an example to verify the feasibility of the algorithm,a numerical simulation is carried out and some meaningful conclusions are obtained.

关 键 词：脉冲微分混沌系统 数值模拟 相图 分岔图 POINCARE截面 

分 类 号：O241.8[理学—计算数学] O415.5[理学—数学]