Some recent developments on linear determinacy
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...
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| Format: | Article |
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AIMS Press
2013-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1419 |
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| author | Carlos Castillo-Chavez Bingtuan Li Haiyan Wang |
| author_facet | Carlos Castillo-Chavez Bingtuan Li Haiyan Wang |
| author_sort | Carlos Castillo-Chavez |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-696e74b0caf642549d41f4e7311d6ddd |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-696e74b0caf642549d41f4e7311d6ddd2025-01-24T02:26:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-07-01105&61419143610.3934/mbe.2013.10.1419Some recent developments on linear determinacyCarlos Castillo-Chavez0Bingtuan Li1Haiyan Wang2Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287Department of Mathematics, University of Louisville, Louisville, KY 40292School of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069The 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.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1419ecologypopulation biologydispersalinteger difference integral equationsnonlinear reaction diffusion difference equations. |
| spellingShingle | Carlos Castillo-Chavez Bingtuan Li Haiyan Wang Some recent developments on linear determinacy Mathematical Biosciences and Engineering ecology population biology dispersal integer difference integral equations nonlinear reaction diffusion difference equations. |
| title | Some recent developments on linear determinacy |
| title_full | Some recent developments on linear determinacy |
| title_fullStr | Some recent developments on linear determinacy |
| title_full_unstemmed | Some recent developments on linear determinacy |
| title_short | Some recent developments on linear determinacy |
| title_sort | some recent developments on linear determinacy |
| topic | ecology population biology dispersal integer difference integral equations nonlinear reaction diffusion difference equations. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1419 |
| work_keys_str_mv | AT carloscastillochavez somerecentdevelopmentsonlineardeterminacy AT bingtuanli somerecentdevelopmentsonlineardeterminacy AT haiyanwang somerecentdevelopmentsonlineardeterminacy |