Impulsive state feedback control of a predator–prey model |
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Authors: | Guirong Jiang Qishao Lu |
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Affiliation: | 1. School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;2. Department of Computational Science and Mathematics, Guilin University of Electronic Technology, Guilin 541004, China |
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Abstract: | The dynamics of a predator–prey model with impulsive state feedback control, which is described by an autonomous system with impulses, is studied. The sufficient conditions of existence and stability of semi-trivial solution and positive period-1 solution are obtained by using the Poincaré map and analogue of the Poincaré criterion. The qualitative analysis shows that the positive period-1 solution bifurcates from the semi-trivial solution through a fold bifurcation. The bifurcation diagrams of periodic solutions are obtained by using the Poincaré map, and it is shown that a chaotic solution is generated via a cascade of period-doubling bifurcations. |
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Keywords: | 34A37 92D25 |
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