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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.
MSC:
 34C60 Qualitative investigation and simulation of models (ODE) 34A37 Differential equations with impulses 92D25 Population dynamics (general) 34C25 Periodic solutions of ODE 34D05 Asymptotic stability of ODE
References:
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