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Exactly solvable models of biological invasion

Author: Sergei V Petrovskii; Bai-Lian Li
Publisher: Boca Raton : Chapman & Hall/CRC, 2006.
Series: Chapman & Hall/CRC mathematical biology and medicine series.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:

Demonstrates the advantages and methods of obtaining exact solutions of the equations that describe nonlinear problems encountered in the study of invasive species spread. This work presents a  Read more...

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Genre/Form: Electronic books
Electronic book
Additional Physical Format: Print version:
Petrovskii, Sergei V.
Exactly solvable models of biological invasion.
Boca Raton : Chapman & Hall/CRC, 2006
(DLC) 2005048466
(OCoLC)60500377
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Sergei V Petrovskii; Bai-Lian Li
ISBN: 1420034960 9781420034967 9781584885214 1584885211 1280512970 9781280512971
OCLC Number: 71230112
Description: 1 online resource (217 pages) : illustrations, map.
Contents: INTRODUCTION; Why exactly solvable models are important; Intra- and inter-species interactions and local population dynamics; Basic mechanisms of species transport; Biological invasion: main facts and constituting examples; MODELS OF BIOLOGICAL INVASION; Diffusion-reaction equations; Integral-difference models; Space-discrete models; Stochastic models; Concluding remarks; BASIC METHODS AND RELEVANT EXAMPLES; The Cole-Hopf transformation and the Burgers equation as a paradigm; Further application of the Cole-Hopf transformation; Method of piecewise linear approximation; Exact solutions of a generalized Fisher equation; More about ansatz; SINGLE-SPECIES MODELS; Impact of advection and migration; Accelerating population waves; The problem of critical aggregation; DENSITY-DEPENDENT DIFFUSION; The Aronson-Newman solution and its generalization; Stratified diffusion and the Allee effect; MODELS OF INTERACTING POPULATIONS; Exact solution for a diffusive predator-prey system; Migration waves in a resource-consumer system; SOME ALTERNATIVE AND COMPLEMENTARY APPROACHES; Wave speed and the eigenvalue problem; Convergence of the initial conditions; Convergence and the paradox of linearization; Application of the comparison principle; ECOLOGICAL EXAMPLES AND APPLICATIONS; Invasion of Japanese beetle in the United States; Mount St. Helens recolonization and the impact of predation; Stratified diffusion and rapid plant invasion; APPENDIX: BASIC BACKGROUND MATHEMATICS; Ordinary differential equations and their solutions; Phase plane and stability analysis; Diffusion equation; ; References; Index.
Series Title: Chapman & Hall/CRC mathematical biology and medicine series.
Responsibility: Sergei V. Petrovskii and Bai-Lian Li.

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