Some recent developments on linear determinacy - Carlos Castillo-Chavez; Bingtuan Li; Haiyan Wang (Mathematical Biosciences and Engineering)
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.