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Stochastic delay logistic model under regime switching. (English) Zbl 1251.34099
Summary: 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.
34K60Qualitative investigation and simulation of models
34K50Stochastic functional-differential equations
34K12Growth, boundedness, comparison of solutions of functional-differential equations
34K25Asymptotic theory of functional-differential equations