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Zbl 1222.34057
Zhao, Zhong; Yang, Li; Chen, Lansun
Impulsive perturbations of a predator-prey system with modified Leslie-Gower and Holling type II schemes. (English)
[J] J. Appl. Math. Comput. 35, No. 1-2, 119-134 (2011). ISSN 1598-5865; ISSN 1865-2085/e

The authors investigate the dynamics of an impulsively controlled predator-prey model with modified Leslie-Gower and Holling type II schemes. Choosing the pest birth rate $r_{1}$ as control parameter, the authors show that there exists a globally asymptotically stable pest-eradication periodic solution when $r_{1}$ is less than some critical value $r_{1}^{*}$, and the system is permanent when $r_{1}$ is larger than the critical value $r_{1}^{*}$. By use of standard techniques of bifurcation theory, the authors prove the existence of oscillations in pest and predator. Furthermore, some situations which lead to a chaotic behavior of the system are investigated by means of numerical simulations.
[Xinyu Song (Xinyang)]

MSC 2000:: *34C60 Applications of qualitative theory of ODE
34A37 Differential equations with impulses
92D25 Population dynamics
34C25 Periodic solutions of ODE
34D05 Asymptotic stability of ODE

Keywords: periodic solution; extinction; permanence; bifurcation

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