Oscillation death in diffusively coupled oscillators by local repulsive link

TL;DR

This paper investigates how local repulsive links can induce oscillation death in networks of coupled oscillators, providing analytical conditions and numerical validation across different systems.

Contribution

It introduces the concept of oscillation death caused by local repulsive links and derives analytical conditions for this phenomenon in coupled Landau-Stuart systems.

Findings

Oscillation death occurs due to local repulsive links in coupled oscillators.

Analytical conditions for oscillation death are derived for Landau-Stuart systems.

Numerical simulations confirm oscillation death in chaotic systems like Sprott and Rössler oscillators.

Abstract

A death of oscillation is reported in a network of coupled synchronized oscillators in presence of additional repulsive coupling. The repulsive link evolves as an averaging effect of mutual interaction between two neighboring oscillators due to a local fault and the number of repulsive links grows in time when the death scenario emerges. Analytical condition for oscillation death is derived for two coupled Landau-Stuart systems. Numerical results also confirm oscillation death in chaotic systems such as a Sprott system and the R\"ossler oscillator. We explore the effect in large networks of globally coupled oscillators and find that the number of repulsive links is always fewer than the size of the network.