Fronts and bumps in spatially extended Kuramoto networks

We consider moving fronts and stationary bumps in networks of non-locally coupled phase oscillators. Fronts connect regions of high local synchrony with regions of complete asynchrony, while bumps consist of spatially-localised regions of partially-synchronous oscillators surrounded by complete asynchrony. Using the Ott-Antonsen ansatz we derive non-local differential equations which describe the network dynamics in the continuum limit. Front and bump solutions of these equations are studied by either freezing them in a travelling coordinate frame or analysing them as homoclinic or heteroclinic orbits. Numerical continuation is used to determine parameter regions in which such solutions exist and are stable. (C) 2011 Elsevier B.V. All rights reserved.