Stochastic birhythmicity outside the coexistence region in the Hindmarsh-Rose model

TL;DR

This paper shows that the Hindmarsh-Rose neuron model exhibits noise-induced birhythmicity, fluctuating between two bursting states even outside the deterministic bistable region, linked to the ghost effect near saddle-node bifurcations.

Contribution

It demonstrates stochastic birhythmicity in the Hindmarsh-Rose model beyond the bistable region and provides an analytical stochastic model to explain this phenomenon.

Findings

Stochastic birhythmicity occurs outside the deterministic bistable region.

The phenomenon is associated with the ghost effect near saddle-node bifurcations.

A simple stochastic model reproduces the birhythmicity as a function of noise and parameters.

Abstract

In this work, we demonstrate that the Hindmarsh-Rose model subjected to additive white noise exhibits birhythmicity. Specifically, the system fluctuates between two distinct bursting attractors characterized by different numbers of spikes. This behavior is observed not only within the bistable region bounded by two saddle-node bifurcations of limit cycles but also beyond these boundaries. This phenomenon is associated with the ghost effect, typically observed near deterministic saddle-node bifurcations. We map the region of stochastic birhythmicity in terms of the noise intensity and a key deterministic parameter that controls the dynamics of fast ion channels. To provide an analytical foundation, we introduce a simple stochastic model with a single saddle-node bifurcation. In this model, stochastic birhythmicity is similarly characterized as a function of noise intensity and the control parameter.