Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling

TL;DR

This paper investigates amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling, revealing unique spatial patterns and conditions for global amplitude death, supported by eigenvalue analysis.

Contribution

It demonstrates the occurrence of amplitude death in unidirectionally coupled oscillators and highlights differences from bidirectional coupling, including the ease of achieving global amplitude death.

Findings

Unidirectional coupling leads to amplitude death without partial or local clustering.

Oblique line structures indicate directional signal flow in unidirectional coupling.

Eigenvalue analysis explains the transition to amplitude death as coupling strength varies.

Abstract

We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as coupling strength increases.