Synchronization in networks of nonlinear oscillators with coupling delays

Abstract— We consider the synchronization problem of an arbitrary number of coupled nonlinear oscillators with delays in the interconnections. The emphasis is on coupled Lorenz systems. The network topology is described by a directed graph. Unlike the conventional approach of deriving directly sufficient synchronization conditions, our approach starts from a linearized stability analysis in a (gain, delay) parameter space of a synchronized equilibrium and extracts insights from an analysis of its bifurcations and from the corresponding emerging behavior. Instrumental to this analysis a factorization of the characteristic equation is employed that not only facilitates the analysis and reduces computational cost, but also allows to determine the precise role of the individual agents and the topology of the network in the (in)stability mechanisms. The study reveals fundamental limitations to synchronization and it explains under which conditions on the topology of the network and on th...

• Type: Conference
• Year: 2008
• Where: CDC
• Authors: Wim Michiels, Henk Nijmeijer
• Keywords: CDC 2008, Control Systems, Lorenz Systems, Synchronization, Topology