The Complex Dynamics of a Stochastic Predator-Prey Model
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 qualitativ...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/401031 |
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| 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. |
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| ISSN: | 1085-3375 1687-0409 |