Minimal-speed Of Traveling Waves To A Lotka-volterra Competition System

Studying the interaction between multiple competing species on population dynamics is one of the important issues in mathematical biology.One of typical mathematical models describing inter-species competition is the so-called Lotka-Volterra type competition system.For many evolution equations,it is found that the minimal wave speed of traveling waves is equal to the asymptotic spreading speed,which can be embodied as the invasion speed of the invader.The study of invasion speed is of great significance for the prevention and control of biological invasion,but its specific value is usually difficult to determine,so the speed selection mechanism has become one of the leading topics in the research of the reaction diffusion equations.In addition,the habitats of the population in nature are mostly discrete,therefore,it is of significant practical significance to study the dynamical behaviors of lattice differential system with spatial nonlocal effects.In this thesis,the minimal-speed selection of a three-component competitive diffusion model are studied.The first part of this thesis mainly studies the speed selection of the minimal wave speed of the traveling waves for the lattice differential system.Under the monostable assumption,firstly,the existence of the wavefront solution for the lattice differential system is proved by the method of upper and lower solutions and limit discussion.After transforming the infinite-dimensional dynamical system into a nonlocal scalar equation,based on the upper and lower solutions method and the technique of comparison principle,the general conditions for linear selection and nonlinear selection of minimal wave speed are established.Further,through the construction of upper and lower solutions,several explicit conditions for speed selection are obtained and then we get threshold values on the speed selection of the net growth rate for the differential system.Finally,the conditions obtained above are verified by numerical simulation,and compared with the corresponding results in the known literature.The second part mainly studies the speed selection mechanism of the minimal wave speed for the continuous competition model.After previous research,it is found that different sufficient conditions on the speed selection can be obtained by constructing different upper and lower solutions of the system.Therefore,we construct subtly appropriate upper and lower solutions for a continuous competitive diffusion system,and develop the technique based on the method of the upper and lower solutions together with the comparison principle to prove judgment conditions of the speed selection mechanism and the threshold results of the competition coefficient for the continuous system.Finally,it is found that the obtained conclusions improve or supplement those in the known references by numerical verification.