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A higher-order noise perturbed predator–prey system with fear effect and mixed functional responses

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Abstract

In this contribution, a higher-order stochastically perturbed predator–prey system involving fear effect, Crowley–Martin functional response and a modified Leslie–Gower functional response is investigated. Based on the preliminary lemma as regards global positive solutions, the sufficient criteria ensuring the existence and uniqueness of an ergodic stationary distribution are established by virtue of constructing suitable Lyapounov functions. Later, the exponential extinction of every species indicates that sufficiently large noise intensities are unfavorable to populations’ growth. It is worth mentioning that we study the probability density function of this system near the quasi-positive equilibrium, and further show the approximate expression. Finally, four numerical examples are supplied to support and illustrate our theoretical results. Analytical results clearly reveal that white noise plays a crucial role in the dynamic behaviors of predator and prey.

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Acknowledgements

The authors would like to thank the editor and anonymous referees for their valuable comments and suggestions which have led an improvement of the presentation. The work is supported by National Natural Science Foundation of China (No. 12101211).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hubei Minzu University, Enshi, 445000, Hubei, People’s Republic of China

    Wenwen Zhang, Zhijun Liu & Qinglong Wang

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  1. Wenwen Zhang
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Correspondence to Zhijun Liu.

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Zhang, W., Liu, Z. & Wang, Q. A higher-order noise perturbed predator–prey system with fear effect and mixed functional responses. J. Appl. Math. Comput. 69, 3999–4021 (2023). https://doi.org/10.1007/s12190-023-01912-5

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  • DOI: https://doi.org/10.1007/s12190-023-01912-5

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