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Dynamics of a stochastic Lotka-Volterra model with regime switching

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Abstract

A stochastic Lotka-Volterra system under regime switching is proposed and investigated. First, sufficient conditions for stochastic permanence and extinction of the solution are established. Then the lower- and upper-growth rates of the positive solution are investigated. In addition, the superior limit of the average in time of the sample path of the solution is estimated. The results show that these properties have close relationships with the stationary probability distribution of the Markov chain. Finally, the main results are illustrated by several examples and figures. Some recent results are extended and improved.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Nos. 11301207, 11171081 and 11301112), Natural Science Foundation of Jiangsu Province (No. BK20130411), Natural Science Research Project of Ordinary Universities in Jiangsu Province (No. 13KJB110002).

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  1. School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, P.R. China

    Meng Liu

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  1. Meng Liu
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Correspondence to Meng Liu.

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Liu, M. Dynamics of a stochastic Lotka-Volterra model with regime switching. J. Appl. Math. Comput. 45, 327–349 (2014). https://doi.org/10.1007/s12190-013-0725-6

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  • DOI: https://doi.org/10.1007/s12190-013-0725-6

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