Analysis of a predator-prey model with Holling II functional response concerning impulsive control strategy. (English) Zbl 1089.92060

Liu, Bing; Teng, Zhidong; Chen, Lansun

J. Comput. Appl. Math. 193, No. 1, 347-362 (2006).

Summary: According to biological and chemical control strategies for pest control, we investigate the dynamic behavior of a Holling II functional response predator-prey system concerning an impulsive control strategy by periodically releasing natural enemies and spraying pesticide at different fixed times. By using the Floquet theorem and a small amplitude perturbation method, we prove that there exists a stable pest-eradication periodic solution when the impulsive period is less than some critical value. Further, a condition for the permanence of the system is also given. Numerical results show that the system we consider can take on various kinds of periodic fluctuations and several types of attractor coexistence and is dominated by periodic, quasiperiodic and chaotic solutions, which implies that the presence of pulses makes the dynamic behavior more complex. Finally, we conclude that our impulsive control strategy is more effective than the classical one if we take chemical control efficiently.

MSC:

92D40	Ecology
34C60	Qualitative investigation and simulation of ordinary differential equation models
34D05	Asymptotic properties of solutions to ordinary differential equations
35C05	Solutions to PDEs in closed form
34C25	Periodic solutions to ordinary differential equations

Keywords:

Holling II predator-prey model; impulsive control strategy; extinction; permanence; bifurcation

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