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Impulsive perturbations of a predator-prey system with modified Leslie-Gower and Holling type II schemes. (English) Zbl 1222.34057
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.

34C60Qualitative investigation and simulation of models (ODE)
34A37Differential equations with impulses
92D25Population dynamics (general)
34C25Periodic solutions of ODE
34D05Asymptotic stability of ODE
Full Text: DOI
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