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

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

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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

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 nonlinearmodel spread rates with the spread rates computed from linearized systems with the linearization carried out around the leadingedge of the invasion. A survey that accounts forrecent 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 contributionscovered in this survey are also discussed.
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Keywords ecology; population biology; Dispersal; integer difference integral equations; nonlinear reaction diffusion difference equations.

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

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