Traveling wave solutions for a diffusive predator-prey model with predator saturation and competition

作     者：Lin Zhu Shi-Liang Wu 

作者机构：School of Mathematics and Statistics Xidian University Xi'an Shanxi 710071 P. R. China 

出 版 物：《International Journal of Biomathematics》 (生物数学学报（英文版）)

年 卷 期：2017年第10卷第6期

页      面：231-253页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Natural Science Foundation of China, NSFC, (11671315) Fundamental Research Funds for the Central Universities, (JB160714, JBG160706) 

主　　题：Diffusive predator prey model traveling wave solution shooting argument Wazewski's set LaSalle's invariance principle. 

摘      要：The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.