Dynamics of a two-prey one-predator system with Watt-type functional response and impulsive control strategy

In this paper, by using theories and methods of ecology and ODE, a two-prey one-predator system with Watt-type functional response and impulsive perturbations on the predator is established. The system is affected by impulse which can be considered as a control. Conditions for the permanence of the system are obtained. The numerical analysis is carried out to study the effects of perturbation varying parameters of the system. The system shows the rich dynamic behavior including quasi-periodic oscillation, narrow periodic window, wide periodic window, chaotic bands, period doubling bifurcation, symmetry-breaking pitchfork bifurcation, period-halving bifurcation and crises, etc.