Effects of different initial conditions on the emergence of chimera states

Abstract

Chimeras are fascinating spatiotemporal states that emerge in coupled oscillators. These states are characterized by the coexistence of coherent and incoherent dynamics, and since their discovery, they have been observed in a rich variety of different systems. Here, we consider a system of non-locally coupled three-dimensional dynamical systems, which are characterized by the coexistence of fixed-points, limit cycles, and strange attractors. This coexistence creates an opportunity to study the effects of different initial conditions – from different basins of attraction – on the emergence of chimera states. By choosing initial conditions from different basins of attraction, and by varying also the coupling strength, we observe different spatiotemporal solutions, ranging from chimera states to synchronous, imperfect synchronous, and asynchronous states. We also determine conditions, in dependence on the basins of attraction, that must be met for the emergence of chimera states.