Stability of reaction–diffusion systems with stochastic switching

Abstract

In this paper, we investigate the stability for reaction systems with stochastic switching. Two types of switched models are considered: (i) Markov switching and (ii) independent and identically distributed switching. By means of the ergodic property of Markov chain, Dynkin formula and Fubini theorem, together with the Lyapunov direct method, some sufficient conditions are obtained to ensure that the zero solution of reaction–diffusion systems with Markov switching is almost surely exponential stable or exponentially stable in the mean square. By using Theorem 7.3 in [R. Durrett, Probability: Theory and Examples, Duxbury Press, Belmont, CA, 2005], we also investigate the stability of reaction–diffusion systems with independent and identically distributed switching. Meanwhile, an example with simulations is provided to certify that the stochastic switching plays an essential role in the stability of systems.