04698nam 22007935 450 991057869780332120230718150059.03-030-98136-310.1007/978-3-030-98136-5(MiAaPQ)EBC7019504(Au-PeEL)EBL7019504(CKB)23931863700041EBL7019504(AU-PeEL)EBL7019504(DE-He213)978-3-030-98136-5(PPN)267814429(EXLCZ)992393186370004120220619d2022 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierDifferential Equations and Population Dynamics I Introductory Approaches /by Arnaud Ducrot, Quentin Griette, Zhihua Liu, Pierre Magal1st ed. 2022.Cham :Springer International Publishing :Imprint: Springer,2022.1 online resource (466 pages)Lecture Notes on Mathematical Modelling in the Life Sciences,2193-4797Description based upon print version of record.Print version: Ducrot, Arnaud Differential Equations and Population Dynamics I Cham : Springer International Publishing AG,c2022 9783030981358 Includes bibliographical references and index.Part 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.This 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.Lecture Notes on Mathematical Modelling in the Life Sciences,2193-4797MathematicsDifferential equationsEpidemiologyMathematical modelsApplications of MathematicsDifferential EquationsEpidemiologyMathematical Modeling and Industrial MathematicsModels matemàticsthubPoblacióthubMalalties infecciosesthubEquacions diferencialsthubLlibres electrònicsthubMathematics.Differential equations.Epidemiology.Mathematical models.Applications of Mathematics.Differential Equations.Epidemiology.Mathematical Modeling and Industrial Mathematics.Models matemàticsPoblacióMalalties infecciosesEquacions diferencials304.60151304.60151Ducrot Arnaud1242322MiAaPQMiAaPQMiAaPQBOOK9910578697803321Differential equations and population dynamics I2998892UNINA