Journal of Mathematical Biology

, Volume 46, Issue 2, pp 132–152

Existence of traveling wave solutions in a diffusive predator-prey model

  • Jianhua Huang
  • Gang Lu
  • Shigui Ruan

DOI: 10.1007/s00285-002-0171-9

Cite this article as:
Huang, J., Lu, G. & Ruan, S. J. Math. Biol. (2003) 46: 132. doi:10.1007/s00285-002-0171-9

Abstract

 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 R4 and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R4. The methods used to prove the results are the shooting argument and the Hopf bifurcation theorem.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jianhua Huang
    • 1
  • Gang Lu
    • 1
  • Shigui Ruan
    • 2
  1. 1.Department of Mathematics, Central China Normal University, Wuhan 430079, Hubei, P. R. China. e-mail: jhhuang@ccnu.edu.cnCN
  2. 2.Department of Mathematics, University of Miami, P. O. Box 249085, Coral Gables, FL 33124-4250, USA. e-mail: ruan@math.miami.eduUS