Propagation Dynamics Of A Lotka-Volterra Competition Model With Periodic Coefficients And Nonlocal Diffusion

The thesis is devoted to studying the existence,uniqueness,global exponential stability and the value range and sign of bistable wave speed in a Lotka-Volterra competition model with nonlocal diffusion and periodic coefficients.The main contents are as follows:In the first chapter,we introduce the research background and significance of the model,the mathematical notations,preliminary knowledge and some important definitions and lemmas,which are used throughout the thesis.In addition,our main results are summarized at the end of the chapter.In the second chapter,we study the the existence and uniqueness of the bistable traveling waves.We first transform the Lotka-Volterra competition system into a cooperative system by using reversible transformation.Then we can use the method of abstract monotonous dynamical system to prove the existence of traveling waves under some suitable assumptions.Finally,the uniqueness of traveling waves can be proved by constructing upper/lower solutions based on the asymptotic properties of the traveling waves.In the third chapter,we study the global exponential stability of the bistable traveling waves.We first construct a refined squeezing upper and lower solutions to establish the iterative scheme.Consequently,the global exponential stability of the traveling wave solutions is finally proved by the “squeezing” technique.In the fourth chapter,we focus on the bistable wave speed.In order to derive the value range of bistable,we compare the spreading speed of monostable traveling waves of the subsystem and the bistable wave speed by the comparison principle.By establishing the comparison principles on wave speed,we derive the general conditions for determining the sign of bistable wave speed.Moreover,we obtain explicit conditions of the sign of bistable wave speed by using the decay rates of the standing wave(or almost standing wave)to construct functions(i.e.,upper or lower solutions with almost zero speed).Finally,numerical simulation demonstrates our theoretical results.In the last chapter,we present the conclusion and put forward some problems which can be further investigated.