Dynamical Systems and Population Persistence.

Format:

Book

Author/Creator:

Smith, Hal L.

Contributor:

Thieme, Horst R.

Series:

Graduate Studies in Mathematics

Graduate Studies in Mathematics ; v.118

Language:

English

Subjects (All):

Population biology.

Biology--Mathematical models.

Biology.

Local Subjects:

Population biology.

Physical Description:

1 online resource (411 p.)

Other Title:

Graduate Studies in Mathematics

Graduate Studies in Mathematics, Volume 118

Place of Publication:

Providence : American Mathematical Society, 2011.

Language Note:

English

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.

Contents:

""Cover""; ""Title page""; ""Contents""; ""Preface""; ""Introduction""; ""Semiflows on metric spaces""; ""Compact attractors""; ""Uniform weak persistence""; ""Uniform persistence""; ""The interplay of attractors, repellers, and persistence""; ""Existence of nontrivial fixed points via persistence""; ""Nonlinear matrix models: Main act""; ""Topological approaches to persistence""; ""An SI endemic model with variable infectivity""; ""Semiflows induced by semilinear Cauchy problems""; ""Microbial growth in a tubular bioreactor""; ""Dividing cells in a chemostat""

""Persistence for nonautonomous dynamical systems""""Forced persistence in linear Cauchy problems""; ""Persistence via average Lyapunov functions""; ""Tools from analysis and differential equations""; ""Tools from functional analysis and integral equations""; ""Bibliography""; ""Index""; ""Back Cover""

Notes:

Description based upon print version of record.

Description based on print version record.

Includes bibliographical references and index.

ISBN:

1-4704-1180-6