oscillator death

The particular properties of dynamics are discussed for dissipatively coupled van der Pol oscillators, non­identical in values of parameters controlling the Andronov–Hopf bifurcation and nonlinear dissipation. Possibility of a special synchronization regime in an infinitively long band between oscillator death and quasiperiodic areas is shown for such system. Non­identity of parameters of nonlinear dissipation results in specific form of the boundary of the main synchronization tongue, which looks like the mirror letter S.

The dynamics of the four dissipatively coupled van der Pol oscillator is considered. Lyapunov chart is presented in the parameter plane and its arrangement is discusses. The effect of increase of the threshold for the «oscillator death» regime and the possibility of complete and partial broadband synchronization are revealed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators, in particular, quasi-periodic saddle-node and Hopf bifurcations.