The Travelling Wave Solutions Of Two Kinds Of Ecological Systems

The phenomena of libration usually happens in the chemical kinetics, bionomics and the disposition of the contamination, as well as the phenomena of disturbance with finite speed. On the other hand, the traveling waves in the form of u(x, t) = u(x - ct) can just behave the two characters. As a result, the traveling waves which describe the diffusion equations from the chemistry and biology become natural and important.In recent years, it is because of the reality background that more and more people have paid attention to the traveling waves of diffusion equations. In the nonlinear diffusion equations, the exist of the traveling waves is an important problem, which usually affects the long-term behavior of the Cauchy-problem.The paper has researched the existence of traveling waves which arc from two kinds of ecological systems. The construction of the paper is as follow.In the first section, the developmental background of the biomathematics is introduced, as well as the definition of Diffusion Equations, the Traveling Waves, and so forth.In the second section, one kind of Lotka-Volterra system whose increasing exponent is restricted by itself and its completers is considered. The existence of the wave fronts is researched, and finally, the sufficient and necessary condition for existence of this kind of solution and critical speed are got.In the third section, a one-dimensional version of reaction-diffusion model with general nonlinear diffusion is considered. The paper researched the character of the trajectory nearby the equilibrium points with the use of target practice, the existence of the equation is got.