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July  2009, 23(3): 1087-1098. doi: 10.3934/dcds.2009.23.1087

Spreading speeds for a partially cooperative 2-species reaction-diffusion model

Hans F. Weinberger 1, , Kohkichi Kawasaki 2, and  Nanako Shigesada 2,

1. 

School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, United States
2. 

Faculty of Culture and Information Science, Doshisha University, Kyotonabe, 610-0321, Japan, Japan

Received  January 2008 Revised  October 2008 Published  November 2008

It is shown that a trick introduced by H. R. Thieme [6] to study a one-species integral equation model with a nonmonotone operator can be used to show that some multispecies reaction-diffusion systems which are cooperative for small population densities but not for large ones have a spreading speed. The ideas are explained by considering a model for the interaction between ungulates and grassland.
Keywords: spreading speed, partially cooperative, reaction-diffusion system.
Mathematics Subject Classification: Primary: 35K45, 35K57, 35B40; Secondary: 92D25, 92D40.
Citation: Hans F. Weinberger, Kohkichi Kawasaki, Nanako Shigesada. Spreading speeds for a partially cooperative 2-species reaction-diffusion model. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 1087-1098. doi: 10.3934/dcds.2009.23.1087
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