Lyapunov Exponents of Hybrid Stochastic Heat Equations

TL;DR

This paper analyzes the stability of hybrid stochastic heat equations by deriving explicit formulas for Lyapunov exponents, showing how Markovian switching can stabilize otherwise unstable systems.

Contribution

It provides explicit formulas for sample and pth moment Lyapunov exponents of hybrid stochastic heat equations and demonstrates stabilization via Markovian switching.

Findings

Explicit formulas for Lyapunov exponents are derived.

Markovian switching can stabilize unstable systems.

Examples illustrate stabilization effects.

Abstract

In this paper, we investigate a class of hybrid stochastic heat equations. By explicit formulae of solutions, we not only reveal the sample Lyapunov exponents but also discuss the $p$th moment Lyapnov exponents. Moreover, several examples are established to demonstrate that unstable (deterministic or stochastic) dynamical systems can be stabilized by Markovian switching.