Stochastic bistable systems, and competing hysteresis and phase coexistence

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.

References in corpus (3)

• A simple mechanism for the reversals of Earth's magnetic field
• The dynamo bifurcation in rotating spherical shells
• Supercriticality to subcriticality in dynamo transitions

Cited by in corpus (1)

• Coexisting Ordered States, Local Equilibrium-like Domains, and Broken Ergodicity in a Non-turbulent Rayleigh-Bénard Convection at Steady-state