Dynamic analysis of a one-prey multi-predator impulsive system with Ivlev-type functional

Considering the Ivlev-type functional response, we develop and analyze a class of one-prey multi-predator system with impulsive effect at different fixed times. Some sufficient conditions ensuring the prey to be extinct are obtained via the Floquent theory and small amplitude perturbation skill. Using the method of comparison involving multiple Laypunov functions, we derive some conditions for the permanence of the system. Numerical simulations of the impulsive system exhibit the rich complex dynamics for the key parameters, such as symmetry-breaking pitchfork bifurcation, periodic doubling bifurcation, chaos, periodic halving cascade and crisis.