%0 Journal Article %1 Castillo-Chavez20131419 %A Castillo-Chavez, C. %A Li, B. %A Wang, H. %D 2013 %J Mathematical Biosciences and Engineering %K Algorithms; Animals; Biological; Computer Dynamics Dynamics; Ecology; Environment; Epidemiology; Humans; Introduced Models, Nonlinear Population Simulation; Species; algorithm; animal; article; biological computer dynamics, ecology; environment; epidemiology; human; introduced model; nonlinear population simulation; species; system; %N 5-6 %P 1419-1436 %R http://dx.doi.org/10.3934/mbe.2013.10.1419 %T Some recent developments on linear determinacy %U http://dx.doi.org/10.3934/mbe.2013.10.1419 %V 10 %X 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.

@article{Castillo-Chavez20131419, 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.}, added-at = {2017-11-10T22:48:29.000+0100}, affiliation = {Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287, United States; School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85282, United States; Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, United States; Biological Statistics and Computational Biology, Cornell University, Ithaca, NY 14853 - 2601, United States; Department of Mathematics, University of Louisville, Louisville, KY 40292, United States; School of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069, United States}, author = {Castillo-Chavez, C. and Li, B. and Wang, H.}, author_keywords = {Dispersal; Ecology; Integer difference integral equations; Nonlinear reaction diffusion difference equations; Population biology}, biburl = {https://www.bibsonomy.org/bibtex/21ae3d4db3270a619988ca9ecacb21a2c/ccchavez}, correspondence_address1 = {Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287, United States}, date-added = {2017-11-10 21:45:26 +0000}, date-modified = {2017-11-10 21:45:26 +0000}, document_type = {Article}, doi = {http://dx.doi.org/10.3934/mbe.2013.10.1419}, interhash = {eac2554f5ad4941f3ffcad47dcfb0ddf}, intrahash = {1ae3d4db3270a619988ca9ecacb21a2c}, issn = {15471063}, journal = {Mathematical Biosciences and Engineering}, keywords = {Algorithms; Animals; Biological; Computer Dynamics Dynamics; Ecology; Environment; Epidemiology; Humans; Introduced Models, Nonlinear Population Simulation; Species; algorithm; animal; article; biological computer dynamics, ecology; environment; epidemiology; human; introduced model; nonlinear population simulation; species; system;}, language = {English}, number = {5-6}, pages = {1419-1436}, pubmed_id = {24245623}, timestamp = {2017-11-10T22:48:29.000+0100}, title = {Some recent developments on linear determinacy}, url = {http://dx.doi.org/10.3934/mbe.2013.10.1419}, volume = 10, year = 2013 }