Synchronization in Networks of Diffusively Time-Delay Coupled (Semi-)Passive Systems

We consider networks with a general topology which consist of nonlinear systems that interact via diffusive coupling with constant time-delays. Using the notion of (semi-)passivity we prove under some mild assumptions that passive systems will synchronize and that the solutions of interconnected semi-passive systems will be bounded. Furthermore we prove that identical strictly semi-passive systems, whose internal dynamics are stable, always will synchronize given that the coupling between the systems is sufficiently strong and a possible constant time delay is sufficiently small. We demonstrate our results using numerical simulations of a network consisting of linear systems and a network consisting Hindmarsh-Rose neurons.