Synchronization in Networks of Diffusively Coupled Nonlinear Systems: Robustness Against Time-Delays
Provides theoretical guarantees for synchronization in time-delayed networks, offering design principles for engineers working with coupled nonlinear systems.
This paper proves that networks of diffusively coupled nonlinear systems with time-delays can synchronize within a unimodal region in the coupling strength vs. time-delay parameter space, and shows how this region scales with network topology to guide robust design.
In this manuscript, we study the problem of robust synchronization in networks of diffusively time-delayed coupled nonlinear systems. In particular, we prove that, under some mild conditions on the input-output dynamics of the systems and the network topology, there always exists a unimodal region in the parameter space (coupling strength versus time-delay), such that if they belong to this region, the systems synchronize. Moreover, we show how this unimodal region scales with the network topology, which, in turn, provides useful insights on how to design the network topology to maximize robustness against time-delays. The results are illustrated by extensive simulation experiments of time-delayed coupled Hindmarsh-Rose neural chaotic oscillators.