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The dynamical behaviors of a Ivlev-type two-prey two-predator system with impulsive effect |
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| Authors: | Xingjie Wu Wei Du Genan Pan Wentao Huang |
| Institution: | 11. Department of Mathematics, Hefei Normal University, Hefei Anhui, 230061, P.R. China 21. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, P.R. China 31. Department of Mathematics and Computational, Huainan Normal University, Huainan Anhui, 232001, P.R. China 41. Department of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin Guangxi, 541004, P.R. China |
| Abstract: | In this paper, considering the strategy of integrated Pest Management (IPM), a class of two-prey two-predator system with the Ivlev-type functional response and impulsive effect at different fixed time is established. By using impulsive comparison theorem, Floquent theory and small amplitude perturbation skill, the sufficient conditions for the system to be extinct of prey and permanence are proved. Moreover, we give two sufficient conditions for the extinction of one of two prey and remaining three species are permanent. Numerical simulation shows that there exist complex dynamics for system, such as symmetry-breaking pitchfork bifurcation, periodic doubling bifurcation, chaos, periodic halving cascade. Lastly, a brief discussion is given. |
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