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The dynamic complexity of a three-species Beddington-type food chain with impulsive control strategy |
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| Authors: | Weiming Wang Hailing Wang Zhenqing Li |
| Institution: | aLaboratory of Quantitative Vegetation Ecology, Institute of Botany, The Chinese Academy of Sciences, Beijing 100093, China bSchool of Mathematics and Information Science, Wenzhou University, Wenzhou Zhejiang 325035, China cSchool of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu Sichuan 610054, China |
| Abstract: | In this paper, by using theories and methods of ecology and ordinary differential equation, the dynamics complexity of 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 Floquet theory of impulsive equation and small amplitude perturbation skills. Furthermore, by using the method of numerical simulation with the international software Maple, the influence of the impulsive perturbations on the inherent oscillation is investigated, which shows rich dynamics, such as quasi-periodic oscillation, narrow periodic window, wide periodic window, chaotic bands, period doubling bifurcation, symmetry-breaking pitchfork bifurcation, period-halving bifurcation and crises, etc. The numerical results indicate that computer simulation is a useful method for studying the complex dynamic systems. |
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