Stochastic Delay Logistic Model under Regime Switching

Abstract

This paper is concerned with a delay logistical model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall's inequality, and Young's inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Also, the relationships between the stochastic permanence and extinction as well as asymptotic estimations of solutions are investigated by virtue of $V$-function technique, $M$-matrix method, and Chebyshev's inequality. Finally, an example is given to illustrate the main results.