耦合Vander Pol-Duffing振子的强共振分叉解

基金项目: 国家自然科学基金(19872010);国家教委博士点基金(98B51125);航空科学基金(98B51125)

Strongly Resonant Bifurcations of Nonlinearly Coupled Van der Pol-Duffing Oscillator

Department of Applied Mathematics and Physics, Beijing University of Aeronautics and Astronautics, Beijing 100083, P R China

摘要: 本文用多尺度方法研究了一非线性耦合Vander Pol-Dufing振子在强共振情形下的分叉解。研究表明,当分叉参数取不同值时,此系统将出现单个振子的周期运动、两个振子的锁频分叉运动和拟周期分叉运动,同时,本文也给出一些数值结果,以验证理论的正确性。
- 非线性耦合 /
- 多尺度法 /
- 锁频 /
- 拟周期
Abstract: In this paper, the strongly resonant bifurcations of a nonlinear coupled Van der Pol-Duffing Oscillator by the classical multi-scale method are studied. It is shown that there exit periodic motions of a single oscillator,frequency-locking and quasi-periodic motions of two oscillators when the parameters vary. Meanwhile, some numerical results are given to test the theoretical ones.
- non-linearly coupling /
- multi-scale method /
- frequency-locking /
- quasi-periodic

[1]	Nayfeh A H.Perturbation Methods[M].New York:Wiley-Interscience,1973
[2]	Nayfeh A H,Mook D T.Nonlinear Oscillations[M].New York:Wiley-Interscience,1979
[3]	Kevorkian J,Cole J D.Perturbation Mathods in Applied Mathematics[M].Springer-Verlag,World Publishing Corporation,1985
[4]	Bogaevski V N,Povzner A.Algebra Methods in Nonlinear Perturbation Theory[M].Springer-Verlag,World Publishing Corporation,1990
[5]	Cheung Y K,Chen S H,Lau S L.A modified Lindstedt-Poincare metheod for certain strongly non-linear oscillators[J].Int J Non-Linear Mech,1991,26(2):367～378
[6]	Chen S H,Cheung Y K.A modified Lindstedt-Poincare method for a stongly non-linear two degree-of-freedom system[J].J S V,1996,193(4):751～762
[7]	Chen H S Y,Chung K W,Xu Z.A perturbation-incremental method for strongly non-linear oscillators[J].Int J Non-Linear Mech,1996,26(1):59～72
[8]	Guckenheimer J,Holmes P.Nonlinear Oscillations,Dynamical Systems,and Bifurcations of Vector Fields[M].Springer-Verlag,World Publishing Corporation,1985
[9]	李炳熙.高维动力系统的周期轨道:理论和应用[M].上海:上海科学技术出版社,1984.