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＜電子ブック＞
Differential Equations and Population Dynamics I : Introductory Approaches / by Arnaud Ducrot, Quentin Griette, Zhihua Liu, Pierre Magal
(Lecture Notes on Mathematical Modelling in the Life Sciences. ISSN:21934797)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
大きさ	XX, 458 p : online resource
著者標目	*Ducrot, Arnaud author Griette, Quentin author Liu, Zhihua author Magal, Pierre author SpringerLink (Online service)
件　名	LCSH:Mathematics LCSH:Differential equations LCSH:Epidemiology LCSH:Mathematical models FREE:Applications of Mathematics FREE:Differential Equations FREE:Epidemiology FREE:Mathematical Modeling and Industrial Mathematics
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-030-98136-5

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