NEFSC Seminar Series

Dr. Daniel Wiley

Howard University

A Fire-Breathing Chimera:  Periodic Incoherence in a Network of Coupled Oscillators

December 18^th 2006,

Steven H. Clark Conference Room

2pm-3pm

Abstract

Networks of identical oscillators have been used to model a wide variety of pattern-forming systems such as neural networks, laser arrays, and coupled biochemical oscillators.  These systems are known to exhibit rich collective behavior, from synchrony and traveling waves to spatiotemporal chaos and incoherence.  Recently, Kuramoto and his colleagues reported a strange new mode of organization which he called coexistence.  Here we will refer to this as the chimera state.  In this chimera state, coherence and incoherence exist side by side in the same system of oscillators.  Such states have never been seen in systems with either local or global coupling; they are apparently peculiar to the intermediate case of nonlocal coupling.  Two techniques are implemented to explain and explore this phenomenon.  In the first method, using a clever choice for the coupling kernel, the system is solved exactly.  In this case the chimera is born via a saddle-node bifurcation.  In the second method the connective topology is simplified and the system is analyzed numerically.  In the latter case, the chimera is born via a Hopf bifurcation.