Stable and transient multicluster oscillation death in nonlocally coupled networks

Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Nov;92(5):052915. doi: 10.1103/PhysRevE.92.052915. Epub 2015 Nov 30.

Abstract

In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multicluster patterns, depending on the cluster distribution prescribed by the initial conditions. Besides stable oscillation death, we also find a regime of long transients asymptotically approaching synchronized oscillations. To explain these phenomena analytically in dependence on the coupling range and the coupling strength, we first use a mean-field approximation, which works well for large coupling ranges but fails for coupling ranges, which are small compared to the cluster size. Going beyond standard mean-field theory, we predict the boundaries of the different stability regimes as well as the transient times analytically in excellent agreement with numerical results.