A Minimal Model of Burst-Noise Induced Bistability

TL;DR

This paper explores how bursty intrinsic noise can induce or destroy bistability in a chemical reaction system, revealing that stochastic effects can qualitatively alter system dynamics without changing the deterministic model.

Contribution

It introduces a minimal model demonstrating how burst noise influences bifurcation behavior, highlighting the role of stochasticity in chemical reaction dynamics.

Findings

Burst size can induce or eliminate saddle-node bifurcations.

Intrinsic noise can qualitatively change system behavior.

Deterministic dynamics remain unchanged despite stochastic effects.

Abstract

We investigate the influence of intrinsic noise on stable states of a one-dimensional dynamical system that shows in its deterministic version a saddle-node bifurcation between monostable and bistable behaviour. The system is a modified version of the Schl\"ogl model, which is a chemical reaction system with only one type of molecule. The strength of the intrinsic noise is varied without changing the deterministic description by introducing bursts in the autocatalytic production step. We study the transitions between monostable and bistable behavior in this system by evaluating the number of maxima of the stationary probability distribution. We find that changing the size of bursts can destroy and even induce saddle-node bifurcations. This means that a bursty production of molecules can qualitatively change the dynamics of a chemical reaction system even when the deterministic description remains unchanged.