Effects of gradient coupling on amplitude death in nonidentical oscillators

TL;DR

This paper explores how gradient coupling influences amplitude death in arrays of nonidentical oscillators, revealing boundary condition-dependent effects and identifying optimal coupling parameters to maximize amplitude death regions.

Contribution

It provides the first analysis of gradient coupling effects on amplitude death under different boundary conditions, including analytical predictions for small systems.

Findings

Gradient coupling enlarges amplitude death domain under no-flux boundaries.

An optimal gradient coupling maximizes amplitude death under periodic boundaries.

Analytical predictions match numerical results for small oscillator arrays.

Abstract

In this work, we investigate gradient coupling effect on amplitude death in an array of N cou- pled nonidentical oscillators with no-flux boundary conditions and periodic boundary conditions respectively. We find that the effects of gradient coupling on amplitude death in diffusive coupled nonidentical oscillators is quite different between those two boundaries conditions. With no-flux boundary conditions, there is a system size related critical gradient coupling $r_c$ within which the gradient coupling tends to monotonically enlarge the amplitude death domain in the parameter space. With the periodical boundary conditions, there is an optimal gradient coupling constant $r_o$ to realize largest AD domain. The gradient coupling first enlarges then decreases the amplitude death domain of diffusive coupled oscillators. The amplitude death domain of parameter space are analytically predicted for small number of gradient coupled oscillators.