On the dynamics of a system of two coupled van der Pol oscillators subjected to a constant excitation force: effects of broken symmetry

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.