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Exactly Solvable Models of Biological Invasion (Paperback)
Loot Price: R1,875
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Exactly Solvable Models of Biological Invasion (Paperback)
Series: Chapman & Hall/CRC Mathematical Biology Series
Expected to ship within 12 - 17 working days
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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.
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