Using critical curves to compute master stability islands for amplitude death in networks of delay-coupled oscillators.

Abstract

In this paper, we present a method to compute master stability islands (MSIs) for amplitude death in networks of delay-coupled oscillators using critical curves. We first demonstrate how critical curves can be used to compute boundaries and contours of MSIs in delay-coupling parameter space and then provide a general study on the effects of the oscillator dynamics and network topology on the number, size, and contour types of all MSIs. We find that the oscillator dynamics can be used to determine the number and size of MSIs and that there are six possible contour types that depend on the choice of oscillator dynamics and the network topology. We introduce contour sequences and use these sequences to study the contours of all MSIs. Finally, we provide example MSIs for several classical nonlinear systems including the van der Pol system, the Rucklidge system, and the Rössler system.