Synchrony and Chimera

In Greek mythology, the chimera was a three-headed, fire-breathing monster---partly lion, partly goat, partly serpent. In the nonlinear dynamics community, however, the chimera state refers to a similarly incongruent pattern, coexistence of coherence and incoherence in networks of coupled oscillators. The chimera phenomenon has fundamental implications that the processes occurring in nature favor a less symmetric configuration, although the underlying principles can be symmetric. Such chimera states have attracted great interest and have been the subject of intensive theoretical investigations in the context of the spontaneous symmetry-breaking. An important goal of this book is to explore further symmetry-broken states beyond the chimera state in the oscillator systems. The chimera phenomena illustrate how structured dynamical patterns (i.e., nonuniform synchronization) can emerge from structureless (i.e.,uniform) system, which is reciprocal to the concept of synchronization that explains how uniform behavior emerges in populations of nonuniform oscillators. We present rigorous analysis for the synchrony and symmetry-broken states in a variety of network topologies of oscillators.