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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 NameAffiliation
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.