Qualitative structure of a discrete predator-prey model with nonmonotonic functional response | Zendy

Yanlin Zhang | Zendy; Qi Cheng | Zendy; Shengfu Deng | Zendy

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Qualitative structure of a discrete predator-prey model with nonmonotonic functional response

Author(s) -

Yanlin Zhang,

Qi Cheng,

Shengfu Deng

Publication year - 2022

Publication title -

discrete and continuous dynamical systems - s

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 34

eISSN - 1937-1632

pISSN - 1937-1179

DOI - 10.3934/dcdss.2022065

Subject(s) - mathematics , ordinary differential equation , functional response , degenerate energy levels , eigenvalues and eigenvectors , fixed point , equilibrium point , discrete time and continuous time , mathematical analysis , differential (mechanical device) , differential equation , pure mathematics , predation , predator , physics , paleontology , statistics , thermodynamics , quantum mechanics , biology

In this paper, we study the qualitative structure of a discrete predator-prey model with nonmonotonic functional response near a degenerate fixed point whose eigenvalues are \begin{document}$ \pm1 $\end{document} . Firstly, the model is transformed into an ordinary differential system by using the normal form theory and the Takens's theorem. Then, the qualitative properties of this ordinary differential system near the degenerate equilibrium are analyzed with the blowing-up method. Finally, according to the conjugacy between the discrete model and the time-one mapping of the vector field, the qualitative structure of this discrete model is obtained. Numerical simulations are also given.

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