Analysis of Stochastic Nicholson-Type Delay System under Markovian Switching on Patches

Based on the influence of random environmental perturbations and the patch structure, we propose a stochastic Nicholson-type delay system under Markovian switching on patches. Existence of a global positive solution is studied. Then, we show ultimate boundedness and estimation of the sample Lyapunov exponent of the solution. Furthermore, sufficient conditions for extinction of species are established, which is the main new ingredient of this paper. Finally, some numerical examples are presented. Our results improve and generalize previous related results.