Analysis Of Integrated Pest Management Model With State-dependent Pulse Controls

As a new interdisciplinary subject of mathematics and biology,biological mathematics has made great progress in the past hundred years.Since the impulse might describe the rapid change or jump of a quantity state at some time,the impulsive differential equations was used in constructing mathematics model for the control of population growth.In this paper,the dynamic properties of different models under different state dependent impulsive control are studied.Firstly,a Leslie-Gower modified with Holling-II type functional response function based on the state dependent impulsive control model and a predator-prey model with two state dependent impulsive control are studied.The dynamic behaviors of the system with different functional response functions under different state dependent impulsive control are analyzed.Secondly,a predator-prey model of Holling-III type with two state dependent impulsive control is studied,by using the successor functions,geometric analysis method,Poincare-Bendixson ring domain theorem of impulsive differential equations,the existence of periodic solution is given.The sufficient conditions for the orbital stability of the system are obtained by using stability theory of periodic solutions for impulsive differential equations and similar poincare criterion.