期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 36, 期 -, 页码 65-80出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2015.11.014
关键词
Stochastic predator-prey systems; Harvesting; Stationary distribution and ergodicity; Periodic solution
类别
资金
- NSFC of China [11401584, 11371085]
- Shandong Province Natural Science Foundation [ZR2013AQ023]
- Fundamental Research Funds for the Central Universities [14CX02220A, 15CX08011A]
In this paper, we investigate the dynamics of the stochastic autonomous and non-autonomous predator-prey systems with nonlinear predator harvesting respectively. For the autonomous system, we first give the existence of the global positive solution. Then, in the case of persistence, we prove that there exists a unique stationary distribution and it has ergodicity by constructing a suitable Lyapunov function. The result shows that, the relatively weaker white noise will strengthen the stability of the system, but the stronger white noise will result in the extinction of one or two species. Particularly, for the non-autonomous periodic system, we show that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, numerical simulations illustrate our theoretical results. (C) 2015 Elsevier B.V. All rights reserved.
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