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| 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 |
| 投稿时间：2024-09-23 修订日期：2024-11-17 |
| DOI： |
| 中文关键词: Helmholtz-Duffing-Rayleigh-Liénard振子 广义谐波函数摄动法 极限环 非线性阻尼 |
| 英文关键词:Helmholtz-Duffing-Rayleigh-Lienard oscillator Generalized harmonic perturbation method Limit cycle Nonlinear damping. |
| 基金项目:湖南省教育厅优秀青年基金(21B0419)资助项目 |
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| 中文摘要: |
| 本文提出了一种改进的广义谐波函数摄动法,并研究了一类具有非对称井势和复杂非线性阻尼的Helmholtz-Duffing-Rayleigh-Liénard振子。利用该方法,推导了系统极限环的振幅与系统参数之间的解析关系式；同时,基于微分方程定性理论,建立了该振子极限环特征量的解析表达式。基于上述结果,对系统极限环的全局演化过程进行了定量分析,不仅得到了极限环的振幅与参数的对应关系、极限环的稳定性随振幅的变化关系,还动态的展现了极限环从产生到分岔再到消失的完整参数区间,对描述系统的全局动力学行为具有重要的意义。为了验证本方法的有效性和准确性,本文所得结果均与数值方法所得结果进行了对比,展现了两者之间具有较好的一致性。因此,本文所提方法是可行的,所得结果是可靠的,是对经典摄动方法的一种有效改进,具有一定的理论意义和应用价值。 |
| 英文摘要: |
| In this paper, 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 differential equation. From the above results, the global evolution process of limit cycle can be quantitatively analyzed. Not only acquire the corresponding relationship between the amplitude of limit cycle and system parameters, but also obtain the relationship between the stability of the limit cycle and the variation of its amplitude. These results 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. To verify the validity and accuracy of the proposed method, the results obtained via the proposed method are compared with those obtained by the numerical method. The comparisons show a good agreement between them. Therefore, the method proposed in this paper is feasible and the results obtained are reliable. It is an effective improvement to the classical perturbation method and has certain theoretical and application value. |
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