Existence of traveling wave solutions in a diffusive predator-prey model.
We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R(4) and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R(4). The methods used to prove the results are the shooting argument and the Hopf bifurcation theorem.
Huang
Jianhua
J
Department of Mathematics, Central China Normal University, Wuhan 430079, Hubei, P. R. China. jhhuang@ccnu.edu.cn
Lu
Gang
G
Ruan
Shigui
S
D000818:Animals; D005075:Biological Evolution; D003198:Computer Simulation; D017753:Ecosystem; D008954:Models, Biological; D011156:Population Density; D011157:Population Dynamics; D011235:Predatory Behavior / Q000502:physiology*