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

Mianjian Ruan | Zendy; Chang Li | Zendy; Xianyi Li | Zendy

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

Author(s) -

Mianjian Ruan,

Chang Li,

Xianyi Li

Publication year - 2021

Publication title -

aims mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.329

H-Index - 15

ISSN - 2473-6988

DOI - 10.3934/math.2022174

Subject(s) - functional response , codimension , mathematics , bifurcation , center manifold , predation , transcritical bifurcation , saddle node bifurcation , predator , bifurcation theory , discrete time and continuous time , mathematical analysis , pure mathematics , hopf bifurcation , physics , nonlinear system , statistics , biology , quantum mechanics , paleontology

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.

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