Traveling Wave Solutions For Difusive Predator-prey Type Systems

This thesis focuses on the existence of traveling wave solutions for difusive predator-prey type systems.First of all, a general model is presented in accord with ecological law and allpredator-prey systems through the study of a variety of models and analysis. Thismodel takes the form of partial diferential equations and can be changed into a four-dimensional ordinary diferential system by separating each nonlinear term as the prod-uct of some monotonic functions. Then, based on the analysis of eigenvalues and man-ifolds, we employ Wazewski Theorem to obtain a positive invariant orbit and defne aLyapunov function. By means of LaSalles invariable principle, we obtain the necessaryand sufcient conditions ensuring the system has travelling wave solutions.The paper consists of the following four parts:In the frst chapter, the background, the signifcance and the progress of the studyof predator-prey systems are presented. Then, the research model of this paper is alsosimply introduced.In the second chapter, we state our main results, our proof framework, andWazewski theory, which we will use in the later proof.In the third chapter, we analyze the eigenvalues of the equilibrium of system, fndthe positive invariant orbit using Wazewski theorem, defne the Lyapunov function andfnally employ the LaSalles invariable principle to obtain some important conclusions.In the fourth chapter, we illustrate our main results by their applications to somereal-world models. Compared with some previous results, the authenticities of ourtheoretical results are verifed.