Rich dynamical behaviors of a predator-prey system with state feedback control and a general functional responses

In this paper, we study dynamics of a logistical predator-prey system with state feedback control and a general functional responses. By using the Poincare map, some conditions for the existence and stability of semi-trivial solution and positive periodic solution are obtained. Numerical results are carried out to illustrate the feasibility of our main results, and it is shown that a chaotic solution is generated via a cascade of perioddoubling bifurcations, which implies that the presence of pulses makes the dynamic behavior more complex. Key-Words: Prey-predator system; State feedback control; Periodic solution; Extinction; Bifurcation