Synchronization Bound for Networks of Nonlinear Oscillators

Investigation of synchronization phenomena in networks of coupled nonlinear oscillators plays a pivotal role in understanding the behavior of biological and mechanical systems with oscillatory properties. We derive a general sufficient condition for synchronization of a network of nonlinear oscillators using a nonsmooth Lyapunov function, and we obtain conditions under which synchronization is guaranteed for a network of Fitzhugh-Nagumo (FN) oscillators in biologically relevant model parameter regimes. We incorporate two types of heterogeneity into our study of FN oscillators: 1) the network structure is arbitrary and 2) the oscillators have non-identical external inputs. Understanding the effects of heterogeneities on synchronization of oscillators with inputs provides a promising step toward control of key aspects of networked oscillatory systems.