Spiral Wave Chimera and Twisted State

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 establish a counterpart relationship between the twisted state and spiral chimera state. To this end the framework of this book touches different coupling schemes between oscillators including the nonlocal coupling and distance-dependent time delays interaction. We present rigorous analysis for the existence and stability of symmetry-broken states in a variety of network topologies of oscillators providing a complete bifurcation diagram.