1. Qualitative analysis of a stochastic ratio-dependent predator–prey system
- Author
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Ji, Chunyan, Jiang, Daqing, and Li, Xiaoyue
- Subjects
- *
QUALITATIVE research , *STOCHASTIC difference equations , *PREDATION , *GLOBAL analysis (Mathematics) , *EXISTENCE theorems , *NUMERICAL analysis , *SIMULATION methods & models - Abstract
Abstract: A stochastic ratio-dependent predator–prey model is investigated in this paper. By the comparison theorem of stochastic equations and Itô’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. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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