Impulsive Homoclinic Chaos in Van der Pol Jerk System  

作　　者：丁玉梅 张琪昌 

机构地区：[1]School of Mechanical Engineering, Tianjin University [2]School of Sciences, Tianjin University of Science and Technology

出　　处：《Transactions of Tianjin University》2010年第6期457-460,共4页天津大学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(No. 10872141);Doctoral Foundation of Ministry of Education of China(No. 20060056005);Natural Science Foundation of Tianjin University of Science and Technology (No. 20070210)

摘　　要：A 3D continuous autonomous chaotic system is reported, which contains a cubic term and six system parameters. Basic dynamic properties of the new Van der Pol Jerk system are studied by means of theoretical analysis and numerical simulation. Based on the Silnikov theorem, the chaotic characterisitics of the dynamic system are discussed. Using Cardano formula and series solution of differential equation, eigenvalue problem and the existence of homoclinic orbit are studied. Furthermore, a rigorous proof for th...A 3D continuous autonomous chaotic system is reported, which contains a cubic term and six system parameters. Basic dynamic properties of the new Van der Pol Jerk system are studied by means of theoretical analysis and numerical simulation. Based on the Silnikov theorem, the chaotic characterisitics of the dynamic system are discussed. Using Cardano formula and series solution of differential equation, eigenvalue problem and the existence of homoclinic orbit are studied. Furthermore, a rigorous proof for the existence of Silnikov-sense Smale horseshoes chaos is presented and some conditions which lead to the chaos are obtained. The formation mechanism indicates that this chaotic system has impulsive homoclinic chaos, and numerical simulation demonstrates that there is a route to chaos.

关 键 词：chaotic system homoclinic orbit Silnikov theorem 

分 类 号：O415.5[理学—理论物理]