Traveling Wave Solutions And Entire Solutions For A Three-component Competitive-diffusive Delayed Lattice Dynamical System

Many models in the field of biomathematics can be summarized as reaction-diffusion equations(or systems).The Lotka-Volterra competition system with spatial diffusion is one of the most important models in this field.In recent years,the population dynamics of interactions among multiple competing species has been intensively studied.On one hand,considering that the reproduction of species is affected by pregnancy,environment and maturation process,time delay is inevitable.On the other hand,the habitat of the population in real life may not be continuous.Therefore,it is important to study the effect of time delay and spatial dispersion on the dynamic behaviors of diffusion systems.In this thesis,the traveling wave solutions and entire solutions of a three-component competitive-diffusion delay lattice differential model are studied.The first part of this paper mainly study the traveling wave solutions and the related problems for the delayed lattice differential model.Firstly,the existence of the minimal wave speed for the traveling wave solutions connecting equilibria(1,0,1)and(0,1,0)is proved by Schauder fixed point theorem,monotone iteration technique and the method of upper and lower solutions.Secondly,for sufficiently small intra-specific competition delay,the asymptotic behavior of traveling wave solutions at ±? is established by using Ikehara's theorem.Finally,the strict monotonicity and uniqueness of traveling wave solutions are proved by applying the sliding method when intra-specific competitive delays are zero.In particular,the effects of delays on the minimum wave speed and wave profile decay rate at ±? are investigated.The second part of this paper mainly study the existence and qualitative properties of entire solutions for the delayed lattice differential model.Firstly,based on the exact asymptotic behavior of the traveling wave solutions at ±?,some estimates on the traveling wave solutions are obtained.The existence of entire solution is proved by constructing appropriate upper and lower solutions and combining the comparison principle when all the inter-specific competitive delays are zero.Such entire solutions behave as two traveling fronts moving towards each other from both sides of -axis,which also provide another invasion way of the stronger species to the weak ones.