Dead zones and phase reduction of coupled oscillators

A dead zone in the interaction between two dynamical systems is a region of their joint phase space where one system is insensitive to the changes in the other. These can arise in a number of contexts, and their presence in phase interaction functions has interesting dynamical consequences for the emergent dynamics. In this paper, we consider dead zones in the interaction of general coupled dynamical systems. For weakly coupled limit cycle oscillators, we investigate criteria that give rise to dead zones in the phase interaction functions. We give applications to coupled multiscale oscillators where coupling on only one branch of a relaxation oscillation can lead to the appearance of dead zones in a phase description of their interaction.& nbsp;Published under an exclusive license by AIP Publishing

Automated summary

This paper investigates the phenomenon of dead zones in dynamical systems, exploring conditions under which dead zones can emerge in coupled oscillators and applying these findings to coupled multiscale oscillators. The presence of dead zones in phase interactions functions can lead to interesting dynamical consequences for emergent dynamics.