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2013, 10(5&6): 1419-1436. doi: 10.3934/mbe.2013.10.1419

## 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, United States

Received  October 2012 Revised  April 2013 Published  August 2013

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.
Citation: Carlos Castillo-Chavez, Bingtuan Li, Haiyan Wang. Some recent developments on linear determinacy. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1419-1436. doi: 10.3934/mbe.2013.10.1419
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