Dynamical Systems and Population Persistence

Inbunden, Engelska, 2011

Del i serien Graduate Studies in Mathematics

1 621 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

Beskrivning

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.

Produktinformation

Utgivningsdatum:2011-01-30
Vikt:900 g
Format:Inbunden
Språk:Engelska
Serie:Graduate Studies in Mathematics
Antal sidor:405
Förlag:American Mathematical Society
ISBN:9780821849453

Utforska kategorier

Tillämpad matematik inom Naturvetenskap och teknik

Mer om författaren

Hal L. Smith, Arizona State University, Tempe, AZ, USAHorst R. Thieme, Arizona State University, Tempe, AZ, USA

Innehållsförteckning

PrefaceIntroductionSemiflows on metric spacesCompact attractorsUniform weak persistenceUniform persistenceThe interplay of attractors, repellers, and persistenceExistence of nontrivial fixed points via persistenceNonlinear matrix models: Main actTopological approaches to persistenceAn SI endemic model with variable infectivitySemiflows induced by semilinear Cauchy problemsMicrobial growth in a tubular bioreactorDividing cells in a chemostatPersistence for nonautonomous dynamical systemsForced persistence in linear Cauchy problemsPersistence via average Lyapunov functionsTools from analysis and differential equationsTools from functional analysis and integral equationsBibliographyIndex

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Dynamical Systems and Population Persistence

AvHal L. Smith,Horst R. Thieme

Inbunden, Engelska, 2011

Del i serien Graduate Studies in Mathematics

1 621 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

Beskrivning

Produktinformation

Utgivningsdatum:2011-01-30
Vikt:900 g
Format:Inbunden
Språk:Engelska
Serie:Graduate Studies in Mathematics
Antal sidor:405
Förlag:American Mathematical Society
ISBN:9780821849453

Utforska kategorier

Tillämpad matematik inom Naturvetenskap och teknik

Mer om författaren

Hal L. Smith, Arizona State University, Tempe, AZ, USAHorst R. Thieme, Arizona State University, Tempe, AZ, USA

Innehållsförteckning

PrefaceIntroductionSemiflows on metric spacesCompact attractorsUniform weak persistenceUniform persistenceThe interplay of attractors, repellers, and persistenceExistence of nontrivial fixed points via persistenceNonlinear matrix models: Main actTopological approaches to persistenceAn SI endemic model with variable infectivitySemiflows induced by semilinear Cauchy problemsMicrobial growth in a tubular bioreactorDividing cells in a chemostatPersistence for nonautonomous dynamical systemsForced persistence in linear Cauchy problemsPersistence via average Lyapunov functionsTools from analysis and differential equationsTools from functional analysis and integral equationsBibliographyIndex