An Input-Output approach to the robust synchronization of dynamical systems with an application to the Hindmarsh-Rose neuronal model

Abstract

Motivated by a deeper understanding of the mechanisms involved in neuronal synchronization, we extend an input/output approach recently proposed to analyze networks of nonlinear dynamical operators defined in the extended L2 space. This extension allows to cover a wider class of systems, by tolerating some heterogeneity among the operators involved. We apply this result to a network of heterogeneous Hindmarsh-Rose neurons and provide an analytical justification of rather counter-intuitive synchronization phenomena observed in simulation.