The Complex Dynamics of a Stochastic Predator-Prey Model | Zendy

Xixi Wang | Zendy; Huilin Huang | Zendy; Yongli Cai | Zendy; Weiming Wang | Zendy

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The Complex Dynamics of a Stochastic Predator-Prey Model

Author(s) -

Xixi Wang,

Huilin Huang,

Yongli Cai,

Weiming Wang

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/401031

Subject(s) - mathematics , stability (learning theory) , lyapunov function , stochastic modelling , exponential stability , focus (optics) , series (stratigraphy) , mathematical optimization , mathematical economics , nonlinear system , computer science , statistics , paleontology , physics , quantum mechanics , machine learning , optics , biology

A modified stochastic ratio-dependent Leslie-Gower predator-prey model isformulated 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 constructingLyapunov functions, some qualitative properties are given, such as the existence of global positivesolutions, stochastic boundedness, and the global asymptotic stability. Based on theseresults, we perform a series of numerical simulations and make a comparative analysis of thestability of the model system within deterministic and stochastic environments

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