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Canard Cycles and Homoclinic Orbit of a Leslie–Gower Predator–Prey Model with Allee Effect and Holling Type II Functional Response

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Abstract

We study dynamics of a fast–slow Leslie–Gower predator–prey system with Allee effect and Holling Type II functional response. More specifically, we show some sufficient conditions to guarantee the existence of two positive equilibria of the system and their location, and then we further fully determine their dynamics. Based on geometric singular perturbation theory and the slow–fast normal form, we determine the associated bifurcation curve and observe canard explosion. Besides, we also find a homoclinic orbit to a saddle with slow and fast segments, in which, the stable and unstable manifolds of the saddle are connected under explicit parameters conditions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, People’s Republic of China

    Tianyu Shi & Zhenshu Wen

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  1. Tianyu Shi
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Contributions

T.S. carried out the investigation, prepared figure 1 and wrote the original draft manuscript. Z.W. convinced the study, verified the investigation and wrote the main manuscript. All authors reviewed the manuscript.

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Correspondence to Zhenshu Wen.

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This work is partially supported by the National Natural Science Foundation of China (12071162), the Natural Science Foundation of Fujian Province (No. 2021J01302) and the Fundamental Research Funds for the Central Universities (No. ZQN–802).

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Shi, T., Wen, Z. Canard Cycles and Homoclinic Orbit of a Leslie–Gower Predator–Prey Model with Allee Effect and Holling Type II Functional Response. Qual. Theory Dyn. Syst. 23, 197 (2024). https://doi.org/10.1007/s12346-024-01059-z

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