# Explosive death in nonlinear oscillators coupled by quorum sensing

## TL;DR

This paper investigates how quorum sensing interactions in nonlinear oscillators can cause both gradual and abrupt transitions to death states, revealing explosive death phenomena and hysteresis effects relevant to biological and chemical systems.

## Contribution

It demonstrates that quorum sensing can induce both second-order and first-order explosive death transitions in coupled nonlinear oscillators, highlighting the role of mean-field feedback.

## Key findings

- Explosive death occurs at large oscillation amplitudes.
- Hysteresis widens with increased mean-field feedback.
- Both continuous and abrupt transitions are induced by quorum sensing.

## Abstract

Many biological and chemical systems exhibit collective behavior in response to the change in their population density. These elements or cells communicate with each other via dynamical agents or signaling molecules. In this work, we explore the dynamics of nonlinear oscillators, specifically Stuart-Landau oscillators and Rayleigh oscillators, interacting globally through dynamical agents in the surrounding environment modeled as a quorum sensing interaction. The system exhibits the typical continuous second-order transition from oscillatory state to death state, when the oscillation amplitude is small. However, interestingly, when the amplitude of oscillations is large we find that the system shows an abrupt transition from oscillatory to death state, a transition termed "explosive death". So the quorum-sensing form of interaction can induce the usual second-order transition, as well as sudden first-order transitions. Further in case of the explosive death transitions, the oscillatory state and the death state coexist over a range of coupling strengths near the transition point. This emergent regime of hysteresis widens with increasing strength of the mean-field feedback, and is relevant to hysteresis that is widely observed in biological, chemical and physical processes.