From Two-Cluster State to Chimera

Abstract

This chapter begins with the question “What is a chimera state?”, in light of which the last two decades of research on these states of coexistence of synchrony and incoherence are treated. Particular emphasis is placed on chimeras in coupled multi-component oscillators. Our original research focuses on how chimeras states evolve from two-cluster solutions in Stuart-Landau oscillators with nonlinear global coupling. For the minimal case $$N=4$$ , two distinct types of chimera – with or without symmetry on average in the unsynchronized part of the ensemble – are found to emerge by means of separate bifurcation sequences. The symmetric-on-average type of chimera is found to consistently evolve for large ensemble sizes as well. However, beyond a certain ensemble size in the order of $$N \approx 15$$ , we are unable to produce long-term chimera states with as many unsynchronized as synchronized oscillators. For long simulation times, the intact cluster is consistently found to absorb single oscillators, thereby also becoming more susceptible to perturbations. We conclude the chapter with a brief study of the spatially extended analogue of our model, resulting in a bifurcation sequence similar to that found for purely global coupling.