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Multiple Bifurcations in a Discrete Bazykin Predator–Prey Model with Predator Intraspecific Interactions and Ratio-Dependent Functional Response

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Abstract

A discrete Bazykin predator–prey model with predator intraspecific interactions and ratio-dependent functional response is proposed and investigated. A brief mathematical analysis of the model involves giving fixed points and analyzing local stability. Codimension-one bifurcations such as the transcritical, fold, flip, Neimark-Sacker bifurcations and codimension-two bifurcations, including the fold-flip bifurcation, 1:2, 1:3, and 1:4 strong resonances, are investigated. Accurate theoretical analysis and exquisite numerical simulation are given simultaneously, which support the main content of this manuscript. With the help of several local attraction basins, period, and Lyapunov exponent diagrams, an intriguing set of fascinating dynamics in the two-parameter spaces of integral step size with other parameters is uncovered. The results in this paper reveal that the dynamics of the discrete-time predator–prey system in both single-parameter and two-parameter spaces are inherently rich and complex.

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Acknowledgements

This work is supported by NSF of Shandong Province(ZR2021MA016, ZR2019MA034), National Natural Science Foundation of China(62003189), China Postdoctoral Science Foundation (2020M672024, 2019M652349) and the Youth Creative Team Sci-Tech Program of Shandong Universities(2019KJI007).

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, People’s Republic of China

    Dongpo Hu, Xiao Yu & Chuan Zhang

  2. College of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou, 510665, People’s Republic of China

    Zhaowen Zheng

  3. Institute of Automation, Qufu Normal University, Qufu, 273165, People’s Republic of China

    Ming Liu

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  1. Dongpo Hu
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DH and ML wrote the main manuscript text. XY, CZ and ZZ prepared all the figures. All authors reviewed the manuscript.

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Correspondence to Ming Liu.

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Hu, D., Yu, X., Zheng, Z. et al. Multiple Bifurcations in a Discrete Bazykin Predator–Prey Model with Predator Intraspecific Interactions and Ratio-Dependent Functional Response. Qual. Theory Dyn. Syst. 22, 99 (2023). https://doi.org/10.1007/s12346-023-00780-5

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