Title: Basin stability for chimera states,
Abstract: Chimera states, namely complex spatiotemporal patterns that consist of
coexisting domains of spatially coherent and incoherent dynamics, are
investigated in a network of coupled identical oscillators. These intriguing
spatiotemporal patterns were first reported in nonlocally coupled phase
oscillators, and it was shown that such mixed type behavior occurs only for
specific initial conditions in nonlocally and globally coupled networks. The
influence of initial conditions on chimera states has remained a fundamental
problem since their discovery. In this report, we investigate the robustness of
chimera states together with incoherent and coherent states in dependence on
the initial conditions. For this, we use the basin stability method which is
related to the volume of the basin of attraction, and we consider nonlocally
and globally coupled time-delayed Mackey-Glass oscillators as example.
Previously, it was shown that the existence of chimera states can be
characterized by mean phase velocity and a statistical measure, such as the
strength of incoherence, by using well prepared initial conditions. Here we
show further how the coexistence of different dynamical states can be
identified and quantified by means of the basin stability measure over a wide
range of the parameter space.