The dynamics of a Beddington-type system with impulsive control strategy |
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Authors: | Zhenqing Li Weiming Wang Hailing Wang |
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Institution: | aLaboratory of Quantitative Vegetation Ecology, Institute of Botany, The Chinese Academy of Sciences, Beijing 100093, China bSoftware Engineering Institute of East China Normal University, Shanghai 200062, China cSchool of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China |
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Abstract: | In this paper, by using the theories and methods of ecology and ordinary differential equation, a prey–predator system with Beddington-type functional response and impulsive control strategy is established. Conditions for the system to be extinct are given by using the theories of impulsive equation and small amplitude perturbation skills. It is proved that the system is permanent via the method of comparison involving multiple Liapunov functions. Furthermore, by using the method of numerical simulation, the influence of the impulsive control strategy on the inherent oscillation are investigated, which shows rich dynamics, such as period doubling bifurcation, crises, symmetry-breaking pitchfork bifurcations, chaotic bands, quasi-periodic oscillation, narrow periodic window, wide periodic window, period-halving bifurcation, etc. That will be useful for study of the dynamic complexity of ecosystems. |
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