LEADER 04698nam 22007935 450 001 9910578697803321 005 20230718150059.0 010 $a3-030-98136-3 024 7 $a10.1007/978-3-030-98136-5 035 $a(MiAaPQ)EBC7019504 035 $a(Au-PeEL)EBL7019504 035 $a(CKB)23931863700041 035 $aEBL7019504 035 $a(AU-PeEL)EBL7019504 035 $a(DE-He213)978-3-030-98136-5 035 $a(PPN)267814429 035 $a(EXLCZ)9923931863700041 100 $a20220619d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDifferential Equations and Population Dynamics I $eIntroductory Approaches /$fby Arnaud Ducrot, Quentin Griette, Zhihua Liu, Pierre Magal 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (466 pages) 225 1 $aLecture Notes on Mathematical Modelling in the Life Sciences,$x2193-4797 300 $aDescription based upon print version of record. 311 08$aPrint version: Ducrot, Arnaud Differential Equations and Population Dynamics I Cham : Springer International Publishing AG,c2022 9783030981358 320 $aIncludes bibliographical references and index. 327 $aPart I Linear Differential and Difference Equations: 1 Introduction to Linear Population Dynamics -- 2 Existence and Uniqueness of Solutions -- 3 Stability and Instability of Linear -- 4 Positivity and Perron-Frobenius's Theorem -- Part II Non-Linear Differential and Difference Equations: 5 Nonlinear Differential Equation -- 6 Omega and Alpha Limit -- 7 Global Attractors and Uniformly -- 8 Linearized Stability Principle and Hartman-Grobman's Theorem -- 9 Positivity and Invariant Sub-region -- 10 Monotone semiflows -- 11 Logistic Equations with Diffusion -- 12 The Poincare-Bendixson and Monotone Cyclic Feedback Systems -- 13 Bifurcations -- 14 Center Manifold Theory and Center Unstable Manifold Theory -- 15 Normal Form Theory -- Part III Applications in Population Dynamics: 16 A Holling's Predator-prey Model with Handling and Searching Predators -- 17 Hopf Bifurcation for a Holling's Predator-prey Model with Handling and Searching Predators -- 18 Epidemic Models with COVID-19. 330 $aThis book provides an introduction to the theory of ordinary differential equations and its applications to population dynamics. Part I focuses on linear systems. Beginning with some modeling background, it considers existence, uniqueness, stability of solution, positivity, and the Perron?Frobenius theorem and its consequences. Part II is devoted to nonlinear systems, with material on the semiflow property, positivity, the existence of invariant sub-regions, the Linearized Stability Principle, the Hartman?Grobman Theorem, and monotone semiflow. Part III opens up new perspectives for the understanding of infectious diseases by applying the theoretical results to COVID-19, combining data and epidemic models. Throughout the book the material is illustrated by numerical examples and their MATLAB codes are provided. Bridging an interdisciplinary gap, the book will be valuable to graduate and advanced undergraduate students studying mathematics and population dynamics. 410 0$aLecture Notes on Mathematical Modelling in the Life Sciences,$x2193-4797 606 $aMathematics 606 $aDifferential equations 606 $aEpidemiology 606 $aMathematical models 606 $aApplications of Mathematics 606 $aDifferential Equations 606 $aEpidemiology 606 $aMathematical Modeling and Industrial Mathematics 606 $aModels matemātics$2thub 606 $aPoblaciķ$2thub 606 $aMalalties infeccioses$2thub 606 $aEquacions diferencials$2thub 608 $aLlibres electrōnics$2thub 615 0$aMathematics. 615 0$aDifferential equations. 615 0$aEpidemiology. 615 0$aMathematical models. 615 14$aApplications of Mathematics. 615 24$aDifferential Equations. 615 24$aEpidemiology. 615 24$aMathematical Modeling and Industrial Mathematics. 615 7$aModels matemātics 615 7$aPoblaciķ 615 7$aMalalties infeccioses 615 7$aEquacions diferencials 676 $a304.60151 676 $a304.60151 700 $aDucrot$b Arnaud$01242322 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910578697803321 996 $aDifferential equations and population dynamics I$92998892 997 $aUNINA