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**The complex dynamics of a stochastic predator-prey model.**
*(English)*
Zbl 1253.93142

Summary: A modified stochastic ratio-dependent Leslie-Gower predator-prey model is formulated and analyzed. For the deterministic model, we focus on the existence of equilibria, local, and global stability; for the stochastic model, by applying Itô formula and constructing Lyapunov functions, some qualitative properties are given, such as the existence of global positive solutions, stochastic boundedness, and the global asymptotic stability. Based on these results, we perform a series of numerical simulations and make a comparative analysis of the stability of the model system within deterministic and stochastic environments.

### MSC:

93E20 | Optimal stochastic control |

92D25 | Population dynamics (general) |

37N25 | Dynamical systems in biology |

60H30 | Applications of stochastic analysis (to PDEs, etc.) |

### Keywords:

stochastic ratio-dependent Leslie-Gower predator-prey model; equilibria; local stability; global stability
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\textit{X. Wang} et al., Abstr. Appl. Anal. 2012, Article ID 401031, 24 p. (2012; Zbl 1253.93142)

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### References:

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