Stochastic dynamical analysis in a hybrid bioeconomic system with telephone noise and distributed delay. Issue 8 (May 2020) - Liu, Chao; Wang, Luying; He, Daihai; Li, Mingwei
Highlights: A hybrid stochastic delayed system with herd behavior and exploitation is proposed. Combined dynamic effects of telephone noise and Lévy jumps are investigated. Stochastically ultimate boundedness and asymptotic behavior of system are studied. Existence of a stationary distribution to the positive solution is investigated. Permanence in mean and extinction of the corresponding population are discussed. Abstract: In this paper, a hybrid stochastic prey-predator system with commercial exploitation and distributed delay is established, where combined dynamic effects of telephone noise and Lévy jumps on stochastic population dynamics are taken into accounts. Stochastically ultimate boundedness of the solution is studied. Existence and uniqueness of globally positive solution to the proposed system are investigated. By constructing appropriate stochastic Lyapunov functions, existence of a stationary distribution to the positive solution is discussed. Furthermore, sufficient conditions for permanence in mean and extinction of corresponding population are derived. Numerical simulations are carried out to show consistency with theoretical analysis.