An Impulsively Controlled Predator-Prey System On Fragmented Landscapes

From the standpoint that different pest control tactics should be employed in combination rather than used separately to accomplish successful pest control, we investigate the dynamical behavior of a Holling Ⅱ functional response prey-predator metapopulation system concerning impulsive control strategy on habi-tat fragmentation. By using Floquet theorem and small amplitude perturbation method, we prove that there exists a stable pest-eradication periodic solution when when one of the following three conditions holds. First, the impulsive period is less than a critical value. Second, the impulsive perturbation is larger than a crit-ical value. Last, the fraction of the habitat fragmentation is larger than a critical value. Further, the condition for the permanence of the two species in the system is also provided. Numerical results show that the system we considered has chaos bands, oscillation period solution, and multitude periods solution, and that the dy-namics produced by fragmented landscapes is less complex than the dynamics of an impulsively controlled predator-prey system. Finally, we conclude that habitat fragmentation and impulsive control functioning together on the system is more effective than only the impulsive control strategy on the system.