Amplitude Death in Coupled Oscillators: An Approach from Robust Stability

Abstract

Amplitude death has been intensively investigated in the field of nonlinear science for almost 40 years. In the present article, we review the use of analytical tools for robust stability/control, which have been provided in the field of system control, to obtain the conditions under which amplitude death occurs when the number of oscillators and the network topologies are unknown. Specifically, we explain our results for two representative couplings for inducing amplitude death, dynamical coupling and delayed coupling.