Some recent developments on linear determinacy

Carlos Castillo-Chavez; Bingtuan Li; Haiyan Wang

doi:10.3934/mbe.2013.10.1419

Article Contents

2013, Volume 10, Issue 5&6: 1419-1436. Doi: 10.3934/mbe.2013.10.1419 open access

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Some recent developments on linear determinacy

1.
Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287
2.
Department of Mathematics, University of Louisville, Louisville, KY 40292
3.
School of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069

Received: October 2012

Revised: April 2013

Published: August 2013

Abstract / Introduction Related Papers Cited by

Abstract

The process of invasion is fundamental to the study of the dynamics of ecological and epidemiological systems. Quantitatively, a crucial measure of species' invasiveness is given by the rate at which it spreads into new open environments. The so-called ``linear determinacy'' conjecture equates full nonlinear model spread rates with the spread rates computed from linearized systems with the linearization carried out around the leading edge of the invasion. A survey that accounts for recent developments in the identification of conditions under which linear determinacy gives the ``right" answer, particularly in the context of non-compact and non-cooperative systems, is the thrust of this contribution. Novel results that extend some of the research linked to some the contributions covered in this survey are also discussed.

Keywords:

Dispersal,
integer difference integral equations,
ecology,
population biology,
nonlinear reaction diffusion difference equations.

Mathematics Subject Classification: Primary: 92D25; Secondary: 39A10, 32K45, 34C60.

Citation:

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