Journal of Mathematical Biology
ISSN: 0303-6812 (printed version)
ISSN: 1432-1416 (electronic version)
Table of Contents
Abstract Volume 46 Issue 2 (2003) pp 132-152
Existence of traveling wave solutions in a diffusive predator-prey model
Jianhua Huang (1) (*), Gang Lu (1) (\dagger), Shigui Ruan (2) (‡)
(1) Department of Mathematics, Central China Normal University, Wuhan 430079, Hubei, P. R. China. e-mail: jhhuang@...
(2) Department of Mathematics, University of Miami, P. O. Box 249085, Coral Gables, FL 33124-4250, USA. e-mail: ruan@...
Received: 25 May 2001 / Revised version: 5 August 2002 / Published online: 19 November 2002
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
(*) Research was supported by the National Natural Science Foundations (NNSF) of China.
(\dagger) Research was supported by the National Natural Science Foundations (NNSF) of China.
(‡) Research was partially supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. On leave from the Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5,
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Online publication: February 3, 2003
© Springer-Verlag Berlin Heidelberg 2003