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Strong resonance bifurcations for a discrete-time prey–predator model

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Abstract

The aim of this paper is to introduce a two-dimensional discrete-time prey–predator, identify its fixed points, as well as investigate one- and two-parameter bifurcations. Numerical normal forms are used in bifurcation analysis. For this model, the Neimark-Sacker, period doubling and strong resonance bifurcations are observed. Based on the critical coefficients, the bifurcation scenarios can be identified. Based on numerical continuation methods, we use the MATLAB package MatContM to verify the analytical results and observe complex dynamics up to 16- iterate.

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Funding

This work was supported by National Natural Science Foundation of China (Grant Nos. 11626029), Natural Science Foundation of Anhui Province of China (Grant Nos. 2008085QA09, 1908085MG232) and Scientific Research Foundation of Education Department of Anhui Province of China (Grant No. KJ2021A0482).

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Authors and Affiliations

  1. Business School, Nanjing University, Nanjing, People’s Republic of China

    Bo Li

  2. School of Finance, Anhui University of Finance and Economics, Bengbu, 233030, Anhui, People’s Republic of China

    Bo Li

  3. Department of Mathematics, Faculty of Science, Fasa University, Fasa, Iran

    Zohreh Eskandari

  4. Department of Mathematical Sciences, University of South Africa, Florida, South Africa

    Zakieh Avazzadeh

Authors
  1. Bo Li
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  2. Zohreh Eskandari
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  3. Zakieh Avazzadeh
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Contributions

ZE: Methodology, Conceptualization, Software, Formal analysis, Writing—original draft. ZA: Investigation, Validation, Software, Formal analysis, Writing—original draft. BL: Writing—review & editing, Visualization, Investigation.

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Correspondence to Bo Li.

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Li, B., Eskandari, Z. & Avazzadeh, Z. Strong resonance bifurcations for a discrete-time prey–predator model. J. Appl. Math. Comput. 69, 2421–2438 (2023). https://doi.org/10.1007/s12190-023-01842-2

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  • DOI: https://doi.org/10.1007/s12190-023-01842-2

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