# Dynamical Systems and Population Persistence

##### by Smith, Hal L; Thieme, Horst R.

Material type: BookSeries: Graduate studies in mathematics: v. 118.Publisher: American Mathematical Society, c2011Description: xvii, 405 p. : ill. ; 27 cm.ISBN: 9780821849453 (alk. paper); 9781470425616; 082184945X (alk. paper).Subject(s): Biology -- Mathematical models | Population biologyDDC classification: 515.39 Summary: "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.Item type | Current location | Call number | Status | Date due | Barcode |
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Books |
Central Library, IISER Bhopal
OPAC URL: http://webopac.iiserb.ac.in/ |
515.39 Sm58D (Browse shelf) | Available | G0351 |

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515.39 L989D Dynamical Systems with Applications using Mathematica | 515.39 N131E Elements of dynamical systems: | 515.39 R566I2 Introduction to Dynamical Systems : | 515.39 Sm58D Dynamical Systems and Population Persistence | 515.42 AA75I Introduction to Infinite Ergodic Theory | 515.42 AT46M Measure theory | 515.42 B27M Measure theory and integration |

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.

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