Bifurcation delay, travelling waves and chimera-like states in a network of coupled oscillators

Abstract

We report novel bifurcation delays and chimera-like states in a network of driven FitzHugh-Nagumo (FHN) oscillators, where each oscillator can rotate either clockwise or anticlockwise. Slow variation of the time-dependent parameter of FHN oscillator near the bifurcation point leads to a delay in the bifurcation. The time delay in the bifurcation is independent of the direction of rotation of the system (clockwise or anticlockwise rotation). When the FHN oscillators are coupled via dissimilar variables, then bifurcation delay in the anticlockwise rotating oscillator changes, creating chimera-like structures and also travelling waves at certain coupling strength. Bifurcation preponement is also observed for other range of coupling strengths. Similar results are also observed in networks of van der Pol and Landau-Stuart oscillators suggesting that the phenomenon is general rather than specific to coupled FHN systems.