
Preface  Preview Material  Table of Contents  Supplementary Material 
Graduate Studies in Mathematics 2011; 405 pp; hardcover Volume: 118 ISBN10: 082184945X ISBN13: 9780821849453 List Price: US$75 Member Price: US$60 Order Code: GSM/118 See also: Nonautonomous Dynamical Systems  Peter E Kloeden and Martin Rasmussen The General Topology of Dynamical Systems  Ethan Akin Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems  Hal L Smith Modular Forms and String Duality  Noriko Yui, Helena Verrill and Charles F Doran  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 infinitedimensional as well as to finitedimensional dynamical systems, and to discretetime as well as to continuoustime semiflows. This monograph provides a selfcontained 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 timeheterogeneous persistence results are developed using socalled "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 metapopulation and discretetime nonlinear matrix models of demographic dynamics. Entire chapters are devoted to infinitedimensional examples including an SI epidemic model with variable infectivity, microbial growth in a tubular bioreactor, and an agestructured model of cells growing in a chemostat. Request an examination or desk copy. Readership Graduate students and research mathematicians interested in dynamical systems and mathematical biology. 


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