QUALITATIVE ANALYSIS OF A STOCHASTIC RATIO-DEPENDENT HOLLING-TANNER SYSTEM

doi:10.1016/S0252-9602(18)30758-6

Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (2): 429-440.doi: 10.1016/S0252-9602(18)30758-6

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QUALITATIVE ANALYSIS OF A STOCHASTIC RATIO-DEPENDENT HOLLING-TANNER SYSTEM

Jing FU¹, Daqing JIANG^2,3,4, Ningzhong SHI², Tasawar HAYAT^3,5, Ahmed ALSAEDI³

1. School of Mathematics, Changchun Normal University, Changchun 130032, China;
2. School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun 130024, China;
3. Nonlinear Analysis and Applied Mathematics(NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 121589, Saudi Arabia;
4. College of Science, China University of Petroleum(East China), Qingdao 266580, China;
5. Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan

Received:2016-05-04 Online:2018-04-25 Published:2018-04-25
Supported by:
This work is supported by NSFC of China Grant (11371085) and the Fundamental Research Funds for the Central Universities (15CX08011A).

Abstract

Abstract:

This article addresses a stochastic ratio-dependent predator-prey system with Leslie-Gower and Holling type Ⅱ schemes. Firstly, the existence of the global positive solution is shown by the comparison theorem of stochastic differential equations. Secondly, in the case of persistence, we prove that there exists a ergodic stationary distribution. Finally, numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings.

Key words: Stochastic ratio-dependent Holling-Tanner system, persistence in mean, stationary distribution

Jing FU, Daqing JIANG, Ningzhong SHI, Tasawar HAYAT, Ahmed ALSAEDI. QUALITATIVE ANALYSIS OF A STOCHASTIC RATIO-DEPENDENT HOLLING-TANNER SYSTEM[J].Acta mathematica scientia,Series B, 2018, 38(2): 429-440.

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QUALITATIVE ANALYSIS OF A STOCHASTIC RATIO-DEPENDENT HOLLING-TANNER SYSTEM

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