Traveling Waves For Two Types Of Population Models With Nonlocal Diffusion

In this paper,we consider of travelling waves for two types of population models with nonlocal diffusion.Chapter 1 introduces the research background and previous results.This chapter de-tailed illustrates the developments at home and abroad and the main work in this paper.Chapter 2 mainly studies a population model with nonlocal diffusion(?)J*u(x,t)=?RJ(x-y)u(y,t)dy,u(x,t)and v(x,t)represent activity phase and stationary phase of population density,?1>0 and ?2>0 are conversion rates between the two phases,f(u,u)is reproductive function,D>0 is diffusion coefficient,?1,?2,?3 are delays.By using fixed point theorem and upper-lower solution method,we prove that the population system has traveling wave front when c>c*.Through Laplace transform and Ikehara lemma,we prove the asymptotic behavior of traveling wave front in-?.It is proved that when 0<c<c*,there is no traveling wave front for the system.Through the characteristic equation we analyse the effects of delay ?1,?2,?3 and conversion rates ?,?2 on c*,we obtain the following conclusion:when(?)2f(0,0)>0,c*is an monotone increasing function on ?i;when(?)2f(0,0)= 0,c*is independent of ?1.c*is a monotone increasing function on ?2,?3,and ?1.c*is an monotone decreasing function on 72.Chapter 3 studys the infectious disease model with spatio-temporal delay and nonlocal diffusionS,I represent the population density of the susceptible and infected population.DS,DI are the diffusion coefficients of the susceptible and infected population,?,d represent the birth rate and natural mortality of susceptible population;? is the death rate of infected;? is the recovery rate;a is the rate of infection;? is the percentage of individual who have survived from susceptibles to become infectives.In this chapter,we use Schauder fixed point theorem and upper-lower solution method to prove that there is a traveling wave for the system.