Solitary death in coupled limit-cycle oscillators with higher-order interactions

TL;DR

This paper explores how higher-order interactions in coupled oscillators lead to a novel solitary death state, characterized by a stable, isolated death state distinct from traditional phase transitions, with implications for understanding complex dynamical phenomena.

Contribution

It introduces a new higher-order coupling scheme for oscillators and uncovers a unique solitary death state not reducible to pairwise interactions, expanding the understanding of oscillator death phenomena.

Findings

Discovery of a stable solitary death state induced by higher-order interactions.

Observation of explosive transitions with amplitude surges before death.

Sensitivity of the solitary death state to initial conditions.

Abstract

Coupled limit cycle oscillators with pairwise interactions depict phase transitions to amplitude or oscillation death. This Letter introduces a scheme for higher-order interactions, which can not be decomposed into pairwise interactions. We investigate Stuart Landau oscillators' dynamical evolution under the impression of such a coupling scheme and discover a particular type of oscillator death where a coupling-dependent stable death state, away from the origin, arises in isolation without being accompanied by any other stable state. We call such a state a Solitary death state. Moreover, the explosive transition to the death state is preceded by a surge in amplitude, followed by the revival of the oscillations. Such versatile dynamical states are further enriched with sensitivity to initial conditions. Finally, we point out the resemblance of the results with different dynamical states associated with epileptic seizures.