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

Jing FU; Daqing JIANG; Ningzhong SHI; Tasawar HAYAT; Ahmed ALSAEDI

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

Acta mathematica scientia, Series B >

2018 , Vol. 38 >Issue 2: 429 - 440

DOI: https://doi.org/10.1016/S0252-9602(18)30758-6

Articles

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

Jing FU ,
Daqing JIANG ,
Ningzhong SHI ,
Tasawar HAYAT ,
Ahmed ALSAEDI

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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 date: 2016-05-04

Online 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).

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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

Cite this article

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 . DOI: 10.1016/S0252-9602(18)30758-6

References

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