南华大学学报（自然科学版）2025，Vol.39Issue(2)：58-66,9.DOI:10.19431/j.cnki.1673-0062.2025.02.008
复杂非线性阻尼下Helmholtz-Duffing振子极限环的全局演化
Global Evolution of Limit Cycles of Helmholtz-Duffing Oscillators with Complex Nonlinear Damping
摘要
Abstract
A modified generalized harmonic function perturbation method is proposed.An oscillator with complex nonlinear damping and asymmetric well potential is studied based on this method.Via the method,the analytical relationship between the amplitude of the limit cycle and system parameters is derived.Meanwhile,the analytical expression of characteristic quantity of limit cycle is established based on the qualitative theory of differ-ential equation.From the above results,the global evolution process of limit cycle can be quantitatively analyzed,which dynamically show the complete parameter interval of each limit cycles from its generation to bifurcation to destination.It is of great significance to describe the global dynamic behavior of the system.There is a good agreement between the results obtained by the proposed method and those obtained by the numerical method.The comparisons show a good agreement between them.关键词
Helmholtz-Duffing-Rayleigh-Liénard振子/广义谐波函数摄动法/极限环/非线性阻尼Key words
Helmholtz-Duffing-Rayleigh-Lienard oscillator/generalized harmonic function perturbation method/limit cycle/nonlinear damping分类
数理科学引用本文复制引用
蔡锦,李震波..复杂非线性阻尼下Helmholtz-Duffing振子极限环的全局演化[J].南华大学学报（自然科学版）,2025,39(2):58-66,9.基金项目
湖南省教育厅优秀青年基金资助项目(21B0419) （21B0419）
