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Analysis of the linear determinacy for spread in cooperative models. Open Access

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Author or creator
Weinberger, H.F.
Lewis, M.A.
Li, B.T.
Additional contributors
Subject/Keyword
cooperative model
linear determinacy
linear conjecture
Type of item
Journal Article (Published)
Language
English
Place
Time
Description
The discrete-time recursion system \un+1=Q[\un] with \un(x) a vector of population distributions of species and Q an operator which models the growth, interaction, and migration of the species is considered. Previously known results are extended so that one can treat the local invasion of an equilibrium of cooperating species by a new species or mutant. It is found that, in general, the resulting change in the equilibrium density of each species spreads at its own asymptotic speed, with the speed of the invader the slowest of the speeds. Conditions on Q are given which insure that all species spread at the same asymptotic speed, and that this speed agrees with the more easily calculated speed of a linearized problem for the invader alone. If this is true we say that the recursion has a single speed and is linearly determinate. The conditions are such that they can be verified for a class of reaction-diffusion models.
Date created
2002
DOI
doi:10.7939/R39C6S25J
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© 2002 Springer. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited.
Citation for previous publication
Weinberger, H.F., Lewis, M.A. & Li, B.T. (2002). Analysis of the linear determinacy for spread in cooperative models. JOURNAL OF MATHEMATICAL BIOLOGY, 45(3), 183-218. DOI: 10.1007/s002850200145
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