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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 Name | Affiliation | | 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. |
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