Chaotic Motions of the van der Pol-Duffing Oscillator Subjected to Periodic External and Parametric Excitations with Delayed Feedbacks

作     者：Liang-qiang ZHOU Fang-qi CHEN Liang-qiang ZHOU;Fang-qi CHEN

作者机构：School of MathematicsNanjing University of Aeronautics and AstronauticsNanjing 210016China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2024年第40卷第4期

页      面：1111-1126页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：supported by the National Natural Science Foundation of China(No.11772148,12172166 and 11872201) China Postdoctoral Science Foundation(No.2013T60531) 

主　　题：Van der Pol-Duffing oscillator time delay chaos parametric excitation Melnikov method 

摘      要：Chaotic dynamics of the van der Pol-Duffing oscillator subjected to periodic external and parametric excitations with delayed feedbacks are investigated both analytically and numerically in this *** the Melnikov method,the critical value of chaos arising from homoclinic or heteroclinic intersections is derived *** feature of the critical curves separating chaotic and non-chaotic regions on the excitation frequency and the time delay is investigated analytically in *** monotonicity of the critical value to the excitation frequency and time delay is obtained *** is presented that there may exist a special frequency for this *** this frequency,chaos in the sense of Melnikov may not occur for any excitation *** also exists a uncontrollable time delay with which chaos always occurs for this *** simulations are carried out to verify the chaos threshold obtained by the analytical method.