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| Bifurcation Analysis of a Discrete Predator-Prey Model with Gompertz Growth and Increased Functional Response |
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| KeyWord:Discrete predator-prey system, semidiscretization method, Gompertz growth model, transcritical bifurcation, Neimark-Sacker bifurcation |
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| Abstract: |
| This study examines a discrete predator-prey model that employs a Gompertz growth function for the prey and a Holling type I functional response. Initially, the research explores the existence and local stability of fixed points within the system, employing a fundamental lemma. Subsequently, the conditions necessary for the emergence of transcritical and Neimark-Sacker bifurcations of the system are established through the application of the center manifold theorem and bifurcation theory. Finally, numerical simulations are performed to confirm the existence of the Neimark-Sacker bifurcation. |
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