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| Dynamics of a Discrete Two-species Competitive Model with Michaelies-Menten Type Harvesting in the First Species |
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| KeyWord:Competitive model with Michaelis-Menten type harvesting, semidiscretization method, transcritical bifurcation, period-doubling bifurcation, pitchfork bifurcation |
| Author Name | Affiliation | | Xin Jin | Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang 310023, China | | Xianyi Li | Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang 310023, China |
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| Abstract: |
| In this paper, we use a semidiscretization method to derive a discrete two-species competitive model with Michaelis-Menten type harvesting in the first species. First, the existence and local stability of fixed points of the system are investigated by employing a key lemma. Subsequently, the transcritical bifurcation, period-doubling bifurcation and pitchfork bifurcation of the model are investigated by using the Center Manifold Theorem and bifurcation theory. Finally, numerical simulations are presented to illustrate corresponding theoretical results. |
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