Hopf Bifurcation Analysis and Approximation of Limit Cycle in Coupled Van Der Pol and Duffing Oscillators

JianpingCai; JianheShen

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Hopf Bifurcation Analysis and Approximation of Limit Cycle in Coupled Van Der Pol and Duffing Oscillators

机译：Van Der Pol和Duffing振子耦合的Hopf分叉分析和极限环逼近

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Using Routh-Hurwitz criterion and Hopf bifurcation theorem, stability of the equilibrium points and Hopf bifurcation of coupled van der Pol and Duffing oscillators are investigated. The parametric curve corresponding to Hopf bifurcation and the existence region for the limit cycle in the parameter space are derived. The method of multiple time scales is used to deduce the analytical approximation of the limit cycle, and the accuracy of the analytical approximation is verified by direct numerical integration.

机译：利用Routh-Hurwitz准则和Hopf分叉定理，研究了耦合范德波尔和达芬振子的平衡点的稳定性和Hopf分叉。导出与Hopf分叉相对应的参数曲线和参数空间中极限环的存在区域。用多个时间尺度方法推导极限环的解析近似，并通过直接数值积分验证了解析近似的准确性。

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《The Open Acoustics Journal》 |2008年第1期|共5页
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JianpingCai; JianheShen;
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中图分类预防医学、卫生学;
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1. Delay-Induced Double Hopf Bifurcations in a System of Two Delay-Coupled van der Pol-Duffing Oscillators [J] . Jiang Heping, Zhang Tonghua, Song Yongli International journal of bifurcation and chaos in applied sciences and engineering . 2015,第4期

机译：两个延迟耦合范德波尔-达芬振荡器系统中的延迟诱导双Hopf分叉
2. Nonresonant Hopf bifurcations of a controlled van der Pol-Duffing oscillator [J] . Ji JC Journal of Sound and Vibration . 2006,第1a2期

机译：受控范德波尔-达芬振荡器的非谐振Hopf分叉
3. MULTIPLE SCALES AND ENERGY ANALYSIS OF COUPLED RAYLEIGH-VAN DER POL OSCILLATORS WITH TIME-DELAYED DISPLACEMENT AND VELOCITY FEEDBACK: HOPF BIFURCATIONS AND AMPLITUDE DEATH [J] . Gizem S. Oztepe, S. Roy Choudhury, Ashish Bhatt Far East Journal of Dynamical Systems . 2015,第1期

机译：时滞位移和速度反馈的耦合Rayleigh-van der POL振荡器的多尺度和能量分析：霍普夫分叉和振幅死亡
4. Analytical Solutions for Limit Cycles of the Forced Van Der Pol Duffing Oscillator [C] . Anant Kant Shukla, T. R. Ramamohan, S. Srinivas International Conference of Numerical Analysis and Applied Mathematics . 2014

机译：强制van der Pol Duffing振荡器限制循环的分析解
5. Modeling the Response of Rayleigh - Van Der Pol Oscillators to Stochastic Excitation Near the Hopf Bifurcation [D] . Lu, Bingshen. 2019

机译：绘制瑞利 - 范德波尔振荡器对Hopf分岔附近随机激发的响应
6. Entrainment and synchronization in networks of Rayleigh–van der Pol oscillators with diffusive and Haken–Kelso–Bunz couplings [O] . Francesco Alderisio, Benoît G. Bardy, Mario di Bernardo -1

机译：具有扩散和Haken-Kelso-Bunz耦合的Rayleigh-van der Pol振荡器网络中的夹带和同步
7. Hopf Bifurcation Analysis and Approximation of Limit Cycle in Coupled Van Der Pol and Duffing Oscillators [O] . Jianping Cai, Jianhe Shen 2008

机译：普通Van der Pol和Duffing振荡器中限位周期的HOPF分配分析和近似
8. Perturbation Procedure for the Van Der Pol Oscillator Based on the Hopf Bifurcation Theorem [R] . Mickens, R. E. 1988

机译：基于Hopf分岔定理的Van Der pol振子的扰动过程

Hopf Bifurcation Analysis and Approximation of Limit Cycle in Coupled Van Der Pol and Duffing Oscillators

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