Dynamics of a Predator-Prey System Concerning Biological and Chemical Controls

We investigate an impulsive predator-prey system with Monod-Haldane type functional response and control strategies, especially, biological and chemical controls. Conditions for the stability of the prey-free positive periodic solution and for the permanence of the system are established via the Floquet theory and comparison theorem. Numerical examples are also illustrated to substantiate mathematical results and to show that the system could give birth to various kinds of dynamical behaviors including periodic doubling, and chaotic attractor. Finally, in discussion section, we consider the dynamic behaviors of the system when the growth rate of the prey varies according to seasonal effects.