Research On The Wave Speed Of Three Kinds Of Lotka-Volterra Models

This thesis is devoted to studying the wave speed of the traveling wave solution of three kinds of Lotka-Volterra models.For the reaction diffusion Lotka-Volterra competition model,we deal with the selection mechanism of the minimal speed of its traveling wave solutions.We first establish general conditions under which the linear or nonlinear selection is realized by using the upper and lower method.Then some explicit criteria are derived by subtly constructing formulas of upper and lower solutions,which improve or complement the corresponding results obtained in the known reference.For the reaction diffusion Lotka-Volterra competition model with seasonal succession,we study the selection mechanism of the minimal wave speed of its time periodic traveling wave solutions.It is the first time that the general conditions of linear selection and nonlinear selection have been derived through the comparison principle and the upper-lower solution method.Secondly,according to the decay characteristics of traveling waves,we obtain some explicit conditions for determining the selection mechanism of the minimal wave speed by constructing the formulae for the upper/lower solutions,including the nonlinear selection condition given for the first time and several linear selection conditions.The linear selection results we obtained in this chapter greatly improve the corresponding result in the reference.For a nonlocal dispersal reaction diffusion Lotka-Volterra competition model,we investigate the speed and the asymptotic properties of its bistable traveling wave solutions.Firstly,we establish the value range of the bistable wave speed in terms of spreading speeds of monostable traveling waves in the system.Then,we prove that the bistable wave speed is unique by means of the asymptotic behaviors of the waves near the two stable equilibria.Moreover,comparison principles on wave speeds are established as long as we can find an upper or lower solution with specific speed.To find or control the speed sign of the bistable wave,we utilize the decay rates of the standing wave(or almost standing wave)to construct test functions so that these functions become upper or lower solutions with almost zero speed for the given parameter sets.The obtained results show that the propagation direction can be determined by adjusting the values of system parameters,and thus predict the outcome of species competition.