A generalized competitive system with stochastic perturbations is proposed in this paper,in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process.By theories of stochastic different...A generalized competitive system with stochastic perturbations is proposed in this paper,in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process.By theories of stochastic differential equations,such as comparison theorem,Ito’s integration formula,Chebyshev’s inequality,martingale’s properties,etc.,the existence and the uniqueness of global positive solution of the system are obtained.Then sufficient conditions for the extinction of the species almost surely,persistence in the mean and the stochastic permanence for the system are derived,respectively.Finally,by a series of numerical examples,the feasibility and correctness of the theoretical analysis results are verified intuitively.Moreover,the effects of the intensity of the stochastic perturbations and the speed of the reverse in the Ornstein–Uhlenbeck process to the dynamical behavior of the system are also discussed.展开更多
基金This work is supported by the Sichuan Science and Technology Program under Grant 2017JY0336 and Hunan Science and Technology Program under Grant 2019JJ50399National College Students,Innovation and Entrepreneurship Training Program under Grant S202010619021Longshan Talent Research Fund of Southwest University of Science and Technology under Grants 17LZX670 and 18LZX622.
文摘A generalized competitive system with stochastic perturbations is proposed in this paper,in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process.By theories of stochastic differential equations,such as comparison theorem,Ito’s integration formula,Chebyshev’s inequality,martingale’s properties,etc.,the existence and the uniqueness of global positive solution of the system are obtained.Then sufficient conditions for the extinction of the species almost surely,persistence in the mean and the stochastic permanence for the system are derived,respectively.Finally,by a series of numerical examples,the feasibility and correctness of the theoretical analysis results are verified intuitively.Moreover,the effects of the intensity of the stochastic perturbations and the speed of the reverse in the Ornstein–Uhlenbeck process to the dynamical behavior of the system are also discussed.
