定点脉冲信号作用下Duffing-Rayleigh系统的混沌预测  

Chaos prediction of Duffing-Rayleigh system excited by fixed impulsive signals

作　　者：牛玉俊[1] 乔俊峰[1] 胡双年 NIU Yujun;QIAO Junfeng;HU Shuangnian(School of Mathematics and Science,Nanyang Institute of Technology,Nanyang 473004,China)

机构地区：[1]南阳理工学院数理学院,河南南阳473004

出　　处：《合肥工业大学学报（自然科学版）》2020年第12期1718-1722,共5页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(U1504105);陕西省自然科学基金资助项目(2018JM1044)。

摘　　要：文章采用摄动法研究了定点脉冲系统的Melnikov方法,得到了定点脉冲系统出现Smale马蹄意义下混沌的必要条件,为定点脉冲系统的混沌研究提供了一种解析工具;利用定点脉冲信号作用下Duffing-Rayleigh系统的混沌预测检验了Melnikov函数的有效性,并通过数值模拟验证了理论结果的正确性。Melnikov function of impulsive system excited by fixed position signals is constructed using perturbation method,and the necessary condition of the appearance of chaos in the sense of Smale horseshoe in nonlinear system with fixed impulsive signals is derived,which give an analytical method to the study of impulsive system.Chaos prediction of Duffing-Rayleigh system with fixed impulsive signals is employed to show the effectiveness of the method mentioned in this paper,and the numerical simulation verifies the theoretical result derived by the Melnikov method.

关 键 词：脉冲系统 MELNIKOV方法 摄动法 Duffing-Rayleigh系统 混沌预测 

分 类 号：O415.5[理学—理论物理] O193[理学—物理]