# Stochastic bistable systems, and competing hysteresis and phase coexistence

## TL;DR

This paper presents a unified dynamical framework for stochastic bistable systems, explaining hysteresis, phase coexistence, and the effects of noise and initial conditions on system behavior.

## Contribution

It introduces a mathematical model that captures hysteresis and phase coexistence in stochastic bistable systems, linking noise levels to system dynamics.

## Key findings

- Hysteresis loops shrink with increasing noise.
- Initial conditions influence final system states.
- The model parallels thermodynamic phase transitions.

## Abstract

In this paper we describe the solution of a stochastic bistable system from a dynamical perspective. We show how a single framework with variable noise can explain hysteresis at zero temperature and two-state coexistence in the presence of noise. This feature is similar to the phase transition of thermodynamics. Our mathematical model for bistable systems also explains how the width of a hysteresis loop shrinks in the presence of noise, and how variation in initial conditions can take such systems to different final states.