| Citation: |
Yue Liu, Zhijun Zeng. ANALYSIS OF A PREDATOR-PREY MODEL WITH CROWLEY-MARTIN AND MODIFIED LESLIE-GOWER SCHEMES WITH STOCHASTIC PERTURBATION[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2409-2435. doi: 10.11948/20190144
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ANALYSIS OF A PREDATOR-PREY MODEL WITH CROWLEY-MARTIN AND MODIFIED LESLIE-GOWER SCHEMES WITH STOCHASTIC PERTURBATION
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Abstract
In this paper, we study a nonautonomous predator-prey model with Crowley-Martin and modified Leslie-Gower schemes with stochastic perturbation. The existence of a global positive solution and stochastically ultimate boundedness are obtained. Sufficient conditions are established for extinction, persistence in the mean, and stochastic permanence of the system. Finally, simulations are carried out to verify our results. -
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References
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Yue Liu, Zhijun Zeng. ANALYSIS OF A PREDATOR-PREY MODEL WITH CROWLEY-MARTIN AND MODIFIED LESLIE-GOWER SCHEMES WITH STOCHASTIC PERTURBATION[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2409-2435. doi: 10.11948/20190144
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Figure 1. The figures (a)-(d) depict the extinction of the prey and predator species. (a)
$ \alpha(t) = 0.46+0.04\sin t,\; \beta(t) = 0.46+0.04\sin t $ . (b)$ \alpha(t) = 0,\; \beta(t) = 0.86+0.04\sin t $ . (c)$ \alpha(t) = 0.86+0.04\sin t,\; \beta(t) = 0 $ . (d)$ \alpha(t) = 0,\; \beta(t) = 0 $ . Both of the prey and predator populations go to extinction. -
Figure 2. The prey population is weakly persistent in the mean, whereas the predator species
$ y $ is extinct. - Figure 3. The prey population is strongly persistent in the mean and the predator species y is strongly persistent in the mean.
- Figure 4. The prey population is extinct but the predator species y is strongly persistent in the mean.
- Figure 5. The system (1.1) is stochastically permanent.