Existence, stationary distribution, and extinction of predator-prey system of prey dispersal with stochastic perturbation (Q1925386)
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scientific article; zbMATH DE number 6116415
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence, stationary distribution, and extinction of predator-prey system of prey dispersal with stochastic perturbation |
scientific article; zbMATH DE number 6116415 |
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Existence, stationary distribution, and extinction of predator-prey system of prey dispersal with stochastic perturbation (English)
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18 December 2012
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Summary: We consider a predator-prey model in which the preys disperse among \(n\) patches \((n \geq 2)\) with stochastic perturbation. We show that there is a unique positive solution and find out the sufficient conditions for the extinction to the system with any given positive initial value. In addition, we investigate that there exists a stationary distribution for the system and it has ergodic property. Finally, we illustrate the dynamic behavior of the system with \(n = 2\) via numerical simulation.
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predator-prey model
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stochastic perturbation
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