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Homoclinic Cycle and Homoclinic Bifurcations ofa Predator-prey Model with Impulsive StateFeedback Control
  
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KeyWord:Semi-continuous dynamic system  Semi-continuous dynamic system  Order-1 homoclinic cycle  Homoclinic bifurcation  Order-1 periodic solution
Author NameAffiliation
Tongqian Zhang College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China 
Tong Xu College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China 
Junling Wang College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China 
Zhichao Jiang Fundamental Science Department, North China Institute of Aerospace Engi- neering, Langfang, Hebei 065000, China 
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Abstract:
      In this paper, the homoclinic bifurcation of a predator-prey system with impulsive state feedback control is investigated. By using the geometry theory of semi-continuous dynamic systems, the existences of order-1 homoclinic cycle and order-1 periodic solution are obtained. Then the stability of order-1 periodic solution is studied. At last, an example is presented to illustrate the main results.