Qualitative analysis of a stochastic ratio-dependent predator-prey system

Authors:
Chunyan Ji;Daqing Jiang;Xiaoyue Li
Affiliations:
School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, Jiangsu, PR China and School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, ...;School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, PR China;School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 3
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Abstract

A stochastic ratio-dependent predator-prey model is investigated in this paper. By the comparison theorem of stochastic equations and Ito's formula, we obtain the global existence of a positive unique solution of the ratio-dependent model. Besides, a condition for species to be extinct is given and a persistent condition is established. We also conclude that both the prey population and the ratio-dependent function are stable in time average. In the end, numerical simulations are carried out to confirm our findings.