Dynamic analysis of a predator-prey impulse model with action threshold depending on the density of the predator and its rate of change

Abstract

The concept of an action threshold that depends on predator density and the rate of change is relatively novel and can engender new ideas among scholars studying predator-prey systems more effectively than earlier concepts. On this basis, a predator-prey system with an action threshold based on predator density and its change rate has been established and its dynamic behavior studied. The exact phase set and pulse set of the model were obtained conducting image analysis. The Poincaré map of the model has been constructed and the extreme value points, monotonic interval and immobility points of the Poincaré map have been studied. In addition, the nature of the periodic solution is discussed and we present simulations of the interesting dynamical behavior of the model through the use of numerical examples. An action threshold that depends on the density and rate of change of predators is more reasonable and realistic than techniques proposed in earlier studies, which is significant for the study of control strategies. It is the analytical approach adopted in this paper that allows researchers to explore other generalized predator-prey models more fully and in-depth.

Keywords

• poincaré map
• nonlinear threshold
• state-dependent impulsive system
• periodic solution