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

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【作者】 付静； 蒋达清； 史宁中； Tasawar HAYAT； Ahmed ALSAEDI；

【Author】 Jing FU;Daqing JIANG;Ningzhong SHI;Tasawar HAYAT;Ahmed ALSAEDI;School of Mathematics, Changchun Normal University;School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE,Northeast Normal University;Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University;College of Science, China University of Petroleum (East China);Department of Mathematics, Quaid-i-Azam University;

【机构】 School of Mathematics, Changchun Normal University； School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE,Northeast Normal University； Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University； College of Science, China University of Petroleum (East China)； Department of Mathematics, Quaid-i-Azam University；

【摘要】 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.

【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.

【关键词】 Stochastic ratio-dependent Holling-Tanner system； persistence in mean； stationary distribution；
【Key words】 Stochastic ratio-dependent Holling-Tanner system； persistence in mean； stationary distribution；
【基金】 supported by NSFC of China Grant(11371085);the Fundamental Research Funds for the Central Universities(15CX08011A)
  • 【文献出处】 Acta Mathematica Scientia(English Series) ,数学物理学报(英文版) , 编辑部邮箱 ,2018年02期
  • 【分类号】O175
  • 【被引频次】1
  • 【下载频次】96
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