Dynamical behaviors of a prey-predator system with impulsive control |
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Authors: | Linning Qian Qingguo Meng |
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Affiliation: | a School of Mathematics, Beijing University of Aeronautics & Astronautics, Beijing 100083, China b Department of Mechanics, Tianjin University of Technology & Education, Tianjin 300222, China c Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539, USA |
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Abstract: | In this paper, we study dynamics of a prey-predator system under the impulsive control. Sufficient conditions of the existence and the stability of semi-trivial periodic solutions are obtained by using the analogue of the Poincaré criterion. It is shown that the positive periodic solution bifurcates from the semi-trivial periodic solution through a transcritical bifurcation. A strategy of impulsive state feedback control is suggested to ensure the persistence of two species. Furthermore, a steady positive period-2 solution bifurcates from the positive periodic solution by the flip bifurcation, and the chaotic solution is generated via a cascade of flip bifurcations. Numerical simulations are also illustrated which agree well with our theoretical analysis. |
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Keywords: | Bifurcation Chaos Autonomous systems Periodic solution Prey-predator system Impulsive effect |
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