Impulsive perturbations of a predator-prey system with modified Leslie-Gower and Holling type II schemes (Q2430465)

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.