Holling type II predator–prey model with nonlinear pulse as state-dependent feedback control

Abstract

We propose a Holling II predator–prey model with nonlinear pulse as state-dependent feedback control strategy and then provide a comprehensively qualitative analysis by using the theories of impulsive semi-dynamical systems. First, the Poincaré map is constructed based on the domains of impulsive and phase sets which are defined according to the phase portraits of the model. Second, the threshold conditions for the existence and stability of the semi-trivial periodic solution are given, and subsequently an order-1 periodic solution is generated through the transcritical bifurcation. Furthermore, the different parameter spaces for the existence and stability of an order-1 periodic solution are investigated. In addition, the existence and nonexistence of order-k(k≥2) periodic solutions have been studied theoretically. Moreover, the numerical investigations are presented in order to substantiate our theoretical results and show the complex dynamics of proposed model. Finally, some biological implications of the mathematical results are discussed in the conclusion section.