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