Stable amplitude chimera in a network of coupled Stuart-Landau oscillators

Abstract

In many natural systems, attractive coupling together with repulsive coupling plays a vital role in determining their evolutionary dynamics. We investigate the stabilization of amplitude chimera through repulsive coupling in the presence of attractive coupling in a system of nonlocally coupled oscillators. The nonlocal repulsive coupling can facilitate the emergence of stable amplitude chimera even for random initial conditions contrasting with the earlier investigations, where the amplitude chimera was observed just as a transient state and that too for a specific cluster initial conditions. The stability of the observed amplitude chimera is analyzed using Floquet theory. To elucidate the transition among the distinct dynamical states, we find the average number of inhomogeneous oscillators as a function of the coupling strength and show that the transition among the dynamical states exhibits hysteresis. Further, we deduce analytically the critical stability curve that separates the oscillatory (amplitude chimera and traveling wave) states from the death (multi-incoherent oscillation death, cluster chimera death, cluster oscillation death) states. We also analyze the influence of the nonisochronicity parameter and noise on the stable amplitude chimera. We report that the nonisochronicity parameter favors the traveling wave state from incoherent death through the stable amplitude chimera state.