We consider the dynamics of a system of two coupled van der Pol oscillators whose (inversion) symmetry is broken by a constant excitation force. We investigate the bifurcation structures of the system both with respect to its parameters and the intensity of the excitation force as well using numerical methods. It is found that the forced system experiences rich and complex bifurcation patterns including period-doubling, crises, coexisting bifurcation branches, and hysteresis. Due to the absence of symmetry, the system develops relatively much more complex dynamics which are reflected by the coexistence of multiple (i.e. two, three or four) asymmetric attractors. Moreover, one of the most interesting and striking features of the system considered in this work is the coexistence of periodic and chaotic bubbles of bifurcation for some suitable parameter ranges. This later phenomenon was not reported previously and thus deserves dissemination.

我们考虑由两个耦合的 van der Pol 振荡器组成的系统的动力学，其（反转）对称性被恒定的激励力破坏。我们研究了系统的分叉结构，包括其参数和激发力的强度以及使用数值方法。研究发现，受迫系统经历了丰富而复杂的分叉模式，包括周期倍增、危机、分叉分支并存和滞后。由于缺乏对称性，系统发展出相对复杂得多的动力学，这反映在多个（即两个、三个或四个）不对称吸引子的共存上。而且，在这项工作中考虑的系统最有趣和最引人注目的特征之一是在一些合适的参数范围内，分叉的周期性气泡和混沌气泡共存。这种后来的现象以前没有报道过，因此值得传播。