Traveling Wave Solutions for Some Classes of Diffusive Predator-Prey Models

被引:18
作者
Ding, Wei [1 ]
Huang, Wenzhang [1 ,2 ]
机构
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[2] Univ Alabama, Dept Math Sci, Huntsville, AL 35899 USA
关键词
Diffusive Predator-prey models; Traveling wave; Shooting argument; Liapunov function; Minimum wave speed; LOTKA-VOLTERRA EQUATIONS; SYSTEMS; EXISTENCE; CONNECTION; SPEEDS;
D O I
10.1007/s10884-015-9472-8
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We investigate the traveling wave solutions for some types of diffusive Predator-prey systems, including the models with prey and predator dependent functional response, that have served as models to study the dynamics of Predator-prey interaction. The method used to show the existence of traveling waves and to identify minimum wave speed consists of two steps. First we obtain globally defined solutions by a shooting argument that is a modification of a recently developed method. We then show the convergence of these global solutions to an interior equilibrium point by the construction of a Liapunov function.
引用
收藏
页码:1293 / 1308
页数:16
相关论文
共 18 条
[1]   RUN FOR YOUR LIFE - NOTE ON THE ASYMPTOTIC SPEED OF PROPAGATION OF AN EPIDEMIC [J].
DIEKMANN, O .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1979, 33 (01) :58-73
[3]  
DUNBAR SR, 1983, J MATH BIOL, V17, P11
[4]  
Gadner R., 1991, T AM MATH SOC, V327, P465
[6]   Existence of traveling wave solutions for diffusive predator-prey type systems [J].
Hsu, Cheng-Hsiung ;
Yang, Chi-Ru ;
Yang, Ting-Hui ;
Yang, Tzi-Sheng .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (04) :3040-3075
[7]   Existence of traveling wave solutions in a diffusive predator-prey model [J].
Huang, JH ;
Lu, G ;
Ruan, SG .
JOURNAL OF MATHEMATICAL BIOLOGY, 2003, 46 (02) :132-152
[8]   Traveling Wave Solutions for a Class of Predator-Prey Systems [J].
Huang, Wenzhang .
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2012, 24 (03) :633-644
[9]  
Levin SA, 2005, BIOSCIENCE, V55, P1075, DOI 10.1641/0006-3568(2005)055[1075:SATEOC]2.0.CO
[10]  
2