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Dynamical Behaviors of a Stochastic Food Chain System with Ornstein–Uhlenbeck Process

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Abstract

Considering the important role that food chains play in ecosystems, in this paper, we study a three-species stochastic food chain model in which the growth rates and death rates are governed by Ornstein–Uhlenbeck process. The main purpose of this paper is to study the dynamic properties of the model. We first prove the existence and uniqueness of the global solution to the model. The moment boundedness and asymptotic behavior of the solution are also verified. Secondly, we get the result of extinction of the predators. Then, a sufficient criteria for the existence of the stationary distribution to the system are established by constructing a suitable Lyapunov function. Under the same conditions, it is worth noting that we further obtain the explicit formulas for the mean and the covariance of the probability density function for a linearized system around a equilibrium point. Finally, several numerical simulations are carried out to illustrate the theoretical results.

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Acknowledgements

The authors thank the support of the National Natural Science Foundation of China ( Grant nos. 11801566, 11871473 ) and the Fundamental Research Funds for the Central Universities of China (Grant nos. 18CX02041A, 19CX02059A).

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Authors and Affiliations

  1. College of Science, China University of Petroleum (East China), Qingdao, 266580, People’s Republic of China

    Qing Yang, Xinhong Zhang & Daqing Jiang

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  1. Qing Yang
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  2. Xinhong Zhang
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  3. Daqing Jiang
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Correspondence to Xinhong Zhang.

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Communicated by Anthony Bloch.

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Yang, Q., Zhang, X. & Jiang, D. Dynamical Behaviors of a Stochastic Food Chain System with Ornstein–Uhlenbeck Process. J Nonlinear Sci 32, 34 (2022). https://doi.org/10.1007/s00332-022-09796-8

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