02694cam 2200397 a 450000100090000000300040000900500170001300800410003001000170007102000310008802000180011902000280013703500240016504000110018908200150020010000240021522200280023922200220026722200120028922200160030124500820031726000430039930000350044249000460047750400510052352012680057465000400184265000300188270000350191283000530194790600450200094200120204595500920205799900150214995201320216416425698OSt20160311123150.0100820s2011 riua b 001 0 eng a 2010033476 a9780821849453 (alk. paper) a9781470425616 a082184945X (alk. paper) a(OCoLC)ocn658117196 ciiserb00a515.392221 aSmith, Hal L.98194 amathematical collection aGratis Collection aGratis amathematics10aDynamical Systems and Population Persistence cHal L. Smith, Horst R. Thieme. bAmerican Mathematical Society,cc2011. axvii, 405 p. :bill. ;c27 cm.1 aGraduate studies in mathematics ;vv. 118 aIncludes bibliographical references and index. a"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. 0aBiologyxMathematical models.98195 0aPopulation biology.981961 aThieme, Horst R.,d1948-98197 0aGraduate studies in mathematics ;vv. 118.98198 a7bcbccorignewd1eecipf20gy-gencatlg 2ddccBK bxh00 2010-08-20ixh07 2010-08-20 to Deweyaxh14 2011-04-14 2 copies rec'd., to CIP ver. c7331d7331 00102ddc406515_390000000000000_SM58D70919208aMAINbMAINcGENd2016-03-10o515.39 Sm58DpG0351r2016-03-10w2016-03-10yBK