Chimera States are Fragile under Random Links

Abstract

We study the dynamics of coupled systems, ranging from maps supporting chaotic attractors to nonlinear differential equations yielding limit cycles, under different coupling classes, connectivity ranges and initial states. Our focus is the robustness of chimera states in the presence of a few time-varying random links, and we demonstrate that chimera states are often destroyed, yielding either spatiotemporal fixed points or spatiotemporal chaos, in the presence of even a single dynamically changing random connection. We also study the global impact of random links by exploring the Basin Stability of the chimera state, and we find that the basin size of the chimera state rapidly falls to zero under increasing fraction of random links. This indicates the extreme fragility of chimera patterns under minimal spatial randomness in many systems, significantly impacting the potential observability of chimera states in naturally occurring scenarios.