02550cam a2200385 a 4500
16425698
OSt
20160311123150.0
100820s2011 riua b 001 0 eng
2010033476
9780821849453 (alk. paper)
9781470425616
082184945X (alk. paper)
(OCoLC)ocn658117196
iiserb
515.39
22
Smith, Hal L.
8194
mathematical collection
Gratis Collection
Gratis
mathematics
Dynamical Systems and Population Persistence
Hal L. Smith, Horst R. Thieme.
American Mathematical Society,
c2011.
xvii, 405 p. :
ill. ;
27 cm.
Graduate studies in mathematics ;
v. 118
Includes bibliographical references and index.
"The mathematical theory of persistence answers questions such as which species, in a mathematical model of interacting species, will survive over the long term. It applies to infinite-dimensional as well as to finite-dimensional dynamical systems, and to discrete-time as well as to continuous-time semiflows. This monograph provides a self-contained treatment of persistence theory that is accessible to graduate students. The key results for deterministic autonomous systems are proved in full detail such as the acyclicity theorem and the tripartition of a global compact attractor. Suitable conditions are given for persistence to imply strong persistence even for nonautonomous semiflows, and time-heterogeneous persistence results are developed using so-called 'average Lyapunov functions'. Applications play a large role in the monograph from the beginning. These include ODE models such as an SEIRS infectious disease in a meta-population and discrete-time nonlinear matrix models of demographic dynamics. Entire chapters are devoted to infinite-dimensional examples including an SI epidemic model with variable infectivity, microbial growth in a tubular bioreactor, and an age-structured model of cells growing in a chemostat."--Publisher's description.
Biology
Mathematical models.
8195
Population biology.
8196
Thieme, Horst R.,
1948-
8197
Graduate studies in mathematics ;
v. 118.
8198
7
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xh00 2010-08-20
xh07 2010-08-20 to Dewey
xh14 2011-04-14 2 copies rec'd., to CIP ver.
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