Bifurcation analysis of delay-coupling induced bistability in coupled van der Pol oscillators.

Abstract

It is shown that the coexistence of synchronous and asynchronous states, being typical for chimera states in large networks of coupled oscillators, can be formed in a minimal chain of two coupled van der Pol oscillators with dissipative delay coupling. This means that a stable limit cycle corresponding to synchronization and an attractive two-dimensional torus (quasiperiodicity) related to an incoherence regime of interacting oscillators coexist in the phase space at the same parameter values. Bistability is observed within the main synchronization region in the control parameter plane at the boundary between the locking and suppression regions. This phenomenon emerges as the delay time in the communication channel increases. The bifurcation mechanism of bistability formation is revealed and studied for a system of delay differential equations, its finite-dimensional model of ordinary differential equations, and by using the amplitude and phase approach.