The Stochastic stability of a Logistic model with Poisson white noise |
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Authors: | Duan Dong-Hai Xu Wei Su Jun and Zhou Bing-Chang |
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Institution: | Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China; School of Science, Xi'an University of Science and Technology, Xi'an 710054, China |
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Abstract: | The stochastic stability of a logistic model subjected to the effect of a random natural environment, modeled as Poisson white noise process, is investigated. The properties of the stochastic response are discussed for calculating the Lyapunov exponent, which had proven to be the most useful diagnostic tool for the stability of dynamical systems. The generalised Itô differentiation formula is used to analyse the stochastic stability of the response. The results indicate that the stability of the response is related to the intensity and amplitude distribution of the environment noise and the growth rate of the species. |
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Keywords: | Poisson white noise Ito formula Lyapunov exponent stochastic bifurcation |
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