时滞耦合van der Pol-Duffing振子环的动力学分析

DYNAMICS OF A RING OF COUPLED VAN DER POL-DUFFING OSCILLATORS WITH TIME DELAYS

研究含时滞的大规模van der Pol-Duffing耦合振子系统的非线性动力学.通过讨论特征方程根分布情况确定系统的稳定性,并在耦合时滞和强度平面上给出振幅死亡区域.结合数值算例,揭示同步和异步周期振荡、概周期运动以及混沌吸引子等现象.基于非线性振子电路和时滞电路,构建电路实验平台,有效验证理论和数值结果.研究结果表明,时滞可以显著影响系统动力学特性,如诱发振幅死亡、稳定性切换以及复杂振荡等.

The dynamic behaviors of a delay-coupled ring of van der Pol-Duffing oscillators were studied.The stability and bifurcation of the system were determined by solving the associated characteristic equation.The parametrical regions of amplitude death were shown in the plane of time delay and coupling strength.Case studies were carried out by numerical simulations,which were validated by circuit experiments.It was shown that time delay can give rise to abundant and interesting behaviors,such as amplitude death,different periodic oscillations,quasi-periodic responses,and even chaotic attractors.