
Exactly Solvable Models of Biological Invasion
Chapman & Hall/CRC (Publisher)
1st Edition
Published on 11. September 2019
Book
Paperback/Softback
232 pages
978-0-367-39241-3 (ISBN)
Description
Much of our current knowledge on biological invasion was derived from field studies, but many recent advances relied heavily on mathematics and computing, particularly mathematical modeling. While numerical simulations are clearly a useful approach, they have some serious drawbacks. Approximations errors and the number of parameter values can have a significant impact on the simulation results, the extent of which often remains obscure. Such difficulties do not arise, however, when the problem can be solved analytically.
Exactly Solvable Models of Biological Invasion demonstrates the advantages and methods of obtaining exact solutions of partial differential equations that describe nonlinear problems encountered in the study of invasive species spread. With emphasis on PDEs of diffusion-reaction type, the authors present a comprehensive collection of exactly solvable models and a unified, self-contained description of the relevant mathematical methods. In doing so, they also provide new insight into important issues such as the impact of the Allee effect, the impact of predation, and the interplay between different modes of species dispersal. Full calculation details make this presentation accessible to biologists as well as applied mathematicians, and a range of ecological examples and applications demonstrate the utility of exact methods in practice.
Exact solutions provide an immediate, complete description of system dynamics for a wide class of initial conditions and serve as a convenient tool for testing numerical algorithms and codes used in more specialized studies. This book lays the groundwork for bringing the power of exactly solvable models to bear on real-world ecological problems.
Exactly Solvable Models of Biological Invasion demonstrates the advantages and methods of obtaining exact solutions of partial differential equations that describe nonlinear problems encountered in the study of invasive species spread. With emphasis on PDEs of diffusion-reaction type, the authors present a comprehensive collection of exactly solvable models and a unified, self-contained description of the relevant mathematical methods. In doing so, they also provide new insight into important issues such as the impact of the Allee effect, the impact of predation, and the interplay between different modes of species dispersal. Full calculation details make this presentation accessible to biologists as well as applied mathematicians, and a range of ecological examples and applications demonstrate the utility of exact methods in practice.
Exact solutions provide an immediate, complete description of system dynamics for a wide class of initial conditions and serve as a convenient tool for testing numerical algorithms and codes used in more specialized studies. This book lays the groundwork for bringing the power of exactly solvable models to bear on real-world ecological problems.
More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 13 mm
Weight
363 gr
ISBN-13
978-0-367-39241-3 (9780367392413)
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Schweitzer Classification
Other editions
Additional editions

Sergei V. Petrovskii | Bai-Lian Li
Exactly Solvable Models of Biological Invasion
Book
07/2005
1st Edition
Chapman & Hall/CRC
€206.30
Shipment within 15-20 days

Sergei V. Petrovskii | Bai-Lian Li
Exactly Solvable Models of Biological Invasion
E-Book
07/2005
Chapman & Hall/CRC
€89.99
Available for download

Sergei V. Petrovskii | Bai-Lian Li
Exactly Solvable Models of Biological Invasion
E-Book
07/2005
Chapman and Hall
€89.99
Available for download
Persons
Petrovskii, Sergei V.; Li, Bai-Lian
Content
Models of Biological Invasion. Basic Methods and Relevant Examples. Single-species Models. Density-dependent Diffusion. Models of Interacting Populations. Alternative and Complementary Approaches. Ecological Examples and Applications.