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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 ordinary differential equation models 34A37 Ordinary differential equations with impulses 92D25 Population dynamics (general) 34C25 Periodic solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations
##### Keywords:
periodic solution; extinction; permanence; bifurcation
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##### References:
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