Research On Persistence And Propagation Dynamics Of Impulsive Reaction(-advection)-diffusion Systems

Whether a species can survive in new habitats and spread spread,this is a basic issue of invasion ecology.This topic is mainly discussed from two aspects:on the one hand,in the stage of population establishment,when some individuals are introduced into a new environment,whether the species can establish a population in the invasion place,in other words,whether the population can adapt to the environment and survive for a long time.On the other hand:If a population is able to adapt to a new environment and begin to spread,how does its spread dynamics,that is,how do you get the speed and mode of spread of the invasive population?Many species,such as fish or large mammal populations,exhibit a pulsed birth pattern.Population density dynamics consisted of intra and inter cycle stages.During a growth cycle,the population decrease trend is continuous,while the population increase is discrete between cycles.Impulsive reaction-diffusion system and impulsive reaction-advection-diffusion system are established for the population with seasonal pulse propagation.The effects of Allee effect,overcompensation,and climate change on the propagation dynamics of invasive species are studied by using monotone semiflow theory,upper and lower solution method,monotone dynamic system theory and other techniques.(1)Threshold dynamics and propagation dynamics behavior of an impulsive reactiondiffusion system with Allee effect at propagation stage are studied:By studying the threshold dynamics of the corresponding impulsive ordinary differential system,the rationality of the impulsive reaction-diffusion system with bistable structure is explained.The existence of bistable traveling waves is proved by using monotone semiflow theory.By means of the global convergence theory of monotone systems and the method of upper and lower solutions,the global stability and uniqueness of bistable traveling waves are proved,and the Lyapunov stability of bistable traveling waves is improved to the global exponential stability.(2)The dynamic behavior of an impulsive reaction-advection-diffusion system with Allee effect at diffusion stage is studied.The monotone semiflow method,the upper and lower solution method and the global convergence result of monotone system are firstly extended to the impulsive reaction-advection-diffusion system with bistable structure in high dimensional space.The existence,global stability and uniqueness of bistable traveling wave solutions in the sense of translation are proved.(3)The propagation dynamics of impulsive reaction-diffusion system with nonmonotone growth function are studied.The existence and spreading speed of nonmonotone traveling wave solutions are studied by using monotone semiflow method by constructing an auxiliary system.The upward convergence of oscillating traveling waves is proved by the property of unimodal system.By using monotone semiflow method,the properties of quadratic iterative systems are studied,and the existence,uniqueness and stability of monostable traveling wave solutions in monotone and nonmonotone cases are obtained.(4)The persistence and propagation dynamics of an impulsive reaction-diffusion system with spatial inhomogeneity are studied.A class of impulsive reaction-diffusion model with habitat migration is first established in high-dimensional space.The persistence criterion of the system on bounded domain is proposed,and the existence,uniqueness and global attraction of the positive steady state solution are proved.The persistence criterion of the system is extended from bounded domain to whole space,revealing how habitat movement speed and pulse reproduction(or harvest)rate affect the persistence of the population.It is verified that introduced species that cannot establish local populations in ecology will be eliminated by the environment,so that the invasion phenomenon will not occur.