Oscillation Quenching in Stuart-Landau Oscillators via Dissimilar Repulsive Coupling

TL;DR

This paper investigates how dissimilar and repulsive couplings induce oscillation quenching in Stuart-Landau oscillators, providing a generalized analytical framework applicable to various network configurations and non-identical oscillators.

Contribution

It introduces a novel coupling scheme combining dissimilar and repulsive links, deriving size-independent stability conditions for amplitude death in Stuart-Landau oscillators.

Findings

Analytical conditions for amplitude death derived

Applicable to non-identical oscillators and various coupling schemes

Provides insights into oscillation quenching phenomena

Abstract

Quenching of oscillations, namely amplitude and oscillations death, is an emerging phenomenon exhibited by many real-world complex systems. Here, we introduce a scheme that combines dissimilar couplings and repulsive feedback links for the interactions of Stuart Landau oscillators and analytically derives the conditions required for the amplitude death. Importantly, this analysis is independent of the network size, presents a generalized approach to calculate the stability conditions for various different coupling schemes, and befits for non-identical oscillators as well. Last, we discuss the similarities of the quenching of oscillations phenomenon with the postictal generalized EEG suppression in convulsive seizures.