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

Hans F. Weinberger; Kohkichi Kawasaki; Nanako Shigesada

doi:10.3934/dcds.2009.23.1087

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

Hans F. Weinberger, Kohkichi Kawasaki, Nanako Shigesada

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	1087-1098
Number of pages	12
Journal	Discrete and Continuous Dynamical Systems
Volume	23
Issue number	3
DOIs	https://doi.org/10.3934/dcds.2009.23.1087
State	Published - Mar 2009
Externally published	Yes

Keywords

Partially cooperative
Reaction-diffusion system
Spreading speed

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10.3934/dcds.2009.23.1087

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abstract = "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.",

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AU - Kawasaki, Kohkichi

AU - Shigesada, Nanako

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N2 - 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.

AB - 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.

KW - Partially cooperative

KW - Reaction-diffusion system

KW - Spreading speed

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IS - 3

ER -

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

Abstract

Keywords

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