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- Title
A generalized stochastic competitive system with Ornstein–Uhlenbeck process.
- Authors
Tian, Baodan; Yang, Liu; Chen, Xingzhi; Zhang, Yong
- Abstract
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, Itô'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.
- Subjects
ORNSTEIN-Uhlenbeck process; STOCHASTIC systems; LOTKA-Volterra equations; STOCHASTIC differential equations; MARTINGALES (Mathematics); POSITIVE systems; BIOLOGICAL extinction
- Publication
International Journal of Biomathematics, 2021, Vol 14, Issue 1, pN.PAG
- ISSN
1793-5245
- Publication type
Article
- DOI
10.1142/S1793524521500017