Global dynamics of the periodic logistic system with periodic impulsive perturbations |
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Authors: | Xianning Liu Lansun Chen |
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Affiliation: | a Department of Mathematics, Southwest China Normal University, Chongqing, 400715, PR China b Institute of Mathematics, Academy of Mathematics & System Sciences, Academia Sinica, Beijing, 100080, PR China |
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Abstract: | This paper studies the global behaviors of the periodic logistic system with periodic impulsive perturbations. The results of D.D. Bainov and P.S. Simeonov (1993) are extended and dynamics different from the corresponding continuous system are found. It is shown that the system may have a unique positive periodic solution which is globally asymptotically stable, or go extinct when the two periods are rational dependent. When they are rational independent, the system has no periodic solutions, however, still has a global attractor or go extinct under some conditions. |
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Keywords: | Impulsive perturbation Logistic system Global asymptotical stability Extinction |
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