时滞反馈与多频激励联合作用下Duffing振子的快慢动力学

FAST-SLOW DYNAMICS OF DUFFING OSCILLATOR WITH TIME-DELAY FEEDBACK UNDER MULTI-FREQUENCY EXCITATIONS

研究了状态时滞反馈与多频混合激励联合作用下Duffing振子模型的非线性动力学.通过讨论特征方程根的分布情况,给出了时滞系统Hopf分岔条件,得到时滞量和反馈增益的分岔曲线,揭示了系统稳态解的共存与动力学转迁方式.结合数值算例,揭示系统在不同参数条件下的快慢动力学行为.结果表明,时滞量及其反馈增益可以显著影响系统的多尺度效应,调谐多频激励幅值亦可以改变快慢变流形的动态特性,从而使得Duffing振子产生不同振荡模式下的复杂动力学行为.

The nonlinear dynamics of a Duffing oscillator with time-delay feedback under multi-frequency excitations were studied.By discussing the distribution of the roots of the characteristic equation,the bifurcation conditions of the time-delay system were achieved,and the parametrical regions about the time-delay and feedback gain were obtained,from which the critical transition conditions among different coexisting attractors were revealed.Fast-slow dynamics of the system with different parameters were explored by numerical examples.The results show that the time delay and feed⁃back gain can significantly affect the dynamic characteristics of the multiple time-scale system.Moreover,the excitation amplitude can also change the dynamic feature of the slow manifold,and thus reswit in the complicated dynamic behav⁃iours with different oscillation modes.