Population Dynamics Model Study With Transient And Non-transient Impulse Effects

The biodiversity is destroyed,with the destruction of the ecological environment.However,the human demand on natural resources is increasing.So,having an effective biological resource management strategy is particularly important.The outstanding achievements in population dynamics are one of the main bases for the formulation of biological resource management strategies.And it is of practical significance to study the population dynamics model.Based on the single population model,this paper mainly studies the effects of the transient and non-transient impulsive harvesting on the system.Based on the theory of impulsive differential equation,the new single population model and predator-prey model are established,and the models are analyzed.Finally,the conclusions are further verified by numerical simulation.This paper is divided into the following two partsIn the first part,a single population model with non-transient / transient impulsive harvesting and impulsive diffusion is established.By using impulsive differential equations and stroboscopic mapping theory,the control conditions of population survival,i.e.permanence of the system,are obtained.Results are verified by numerical simulation.In the second part,the stage structured predator-prey model with transient / nontransient impulsive harvesting and birth pulse is studied.the transient and non-transient impulsive harvesting are considered in this system.Meanwhile,in order to be more realistic,the predator is divided into two groups: larvae with no predation ability and adults with predation ability.The comparison theorem is used to analyze the permanence of the system,and the correctness of the conclusion is proved by the corresponding numerical simulation.The final results show that the transient and non-transient impulsive harvesting both play important roles in the persistence of the system.Shortening the non-transient impulsive harvesting interval or controlling the transient impulsive harvesting reasonably has a positive effect on the sustainable survival of the population.