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Research Article | Open Access

Codimension two 1:1 strong resonance bifurcation in a discrete predator-prey model with Holling Ⅳ functional response

Mianjian Ruan1, Chang Li2, Xianyi Li1( )
Department of Big Data Science, School of Science Zhejiang University of Science and Technology, Hangzhou 310023, China
Shenzhen Experimental School, Shenzhen 518028, China
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Abstract

In this paper we revisit a discrete predator-prey model with Holling Ⅳ functional response. By using the method of semidiscretization, we obtain new discrete version of this predator-prey model. Some new results, besides its stability of all fixed points and the transcritical bifurcation, mainly for codimension two 1:1 strong resonance bifurcation, are derived by using the center manifold theorem and bifurcation theory, showing that this system possesses complicate dynamical properties.

Keywords

predator-prey modelholling Ⅳ functional responsetranscritical bifurcation1:1 strong resonance bifurcationcodimension two
CLC number: 39A28, 3AA30

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 3150-3168
DOI: 10.3934/math.2022174

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Cite this article:
Ruan M, Li C, Li X. Codimension two 1:1 strong resonance bifurcation in a discrete predator-prey model with Holling Ⅳ functional response. AIMS Mathematics, 2022, 7(2): 3150-3168. https://doi.org/10.3934/math.2022174

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Received: 29 September 2021
Accepted: 17 November 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)