| Citation: |
Jingliang Lv, Xiaoling Zou, Yujie Li. DYNAMICAL PROPERTIES OF A STOCHASTIC PREDATOR-PREY MODEL WITH FUNCTIONAL RESPONSE[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1242-1255. doi: 10.11948/20190104
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DYNAMICAL PROPERTIES OF A STOCHASTIC PREDATOR-PREY MODEL WITH FUNCTIONAL RESPONSE
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Abstract
A stochastic prey-predator model with functional response is investigated in this paper. A complete threshold analysis of coexistence and extinction is obtained. Moreover, we point out that the stochastic predator-prey model undergoes a stochastic Hopf bifurcation from the viewpoint of numerical simulations. Some numerical simulations are carried out to support our results. -
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References
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Jingliang Lv, Xiaoling Zou, Yujie Li. DYNAMICAL PROPERTIES OF A STOCHASTIC PREDATOR-PREY MODEL WITH FUNCTIONAL RESPONSE[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1242-1255. doi: 10.11948/20190104
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Figure 1. both
$ x $ and$ y $ go extinct -
Figure 2.
$ x $ is persistent and$ y $ goes extinct -
Figure 3. both
$ x $ and$ y $ are persistent -
Figure 4. both
$ x $ and$ y $ go extinct -
Figure 5.
$ x $ is persistent and$ y $ goes extinct -
Figure 6. both
$ x $ and$ y $ are persistent -
Figure 7.
$ x $ goes extinct and$ y $ is persistent -
Figure 8.
$ x $ goes extinct and$ y $ is persistent -
Figure 9. both
$ x $ and$ y $ are persistent - Figure 10. Periodic solution for the system (3.1)
- Figure 11. A stable limit cycle for the system (3.3) in phase space.
- Figure 12. A stable limit cycle for the system (3.3) in three-dimensional space introducing time axis.
- Figure 13. A stable positive equilibrium point for the system (3.4).
- Figure 14. A stable positive equilibrium point for the system (3.4) in phase space.
- Figure 15. A stable positive equilibrium point for the system (3.4) in three-dimensional space introducing time axis.
- Figure 16. A stochastic limit cycle for the system (3.1) in phase space.
- Figure 17. A stochastic limit cycle for the system (3.1) in three-dimensional space introducing time axis.
- Figure 18. A crater-like stationary distribution for the system (3.1) in three-dimensional space.
- Figure 19. A stochastic solution process for the system (3.2) in phase space.
- Figure 20. A stochastic solution process for the system (3.2) in three-dimensional space introducing time axis.
- Figure 21. A peak-like stationary distribution for the system (3.2) in three-dimensional space.