Stability analysis for stochastic complex reaction–diffusion systems with Lévy noise and Markovian switching

Abstract

This paper discuss the mean-square input-to-state stability and mean square integral input-to-state stability for stochastic complex reaction–diffusion systems with Lévy noise and Markovian switching. Sufficient criteria related to the transition rate and coupling forms are introduced through applying multiple Lyapunov functions and an inequality for mathematical expectation is constructed to solve the switch count process. These conditions can be applied to the vast majority of biological models with reaction–diffusion terms where the Gilpin–Ayala model is presented in this paper to demonstrate the practical applicability of the obtained theorem. Finally, a numerical example is given to showcase the effectiveness of our theoretical results.