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Record Nr. |
UNINA9910578697803321 |
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Autore |
Ducrot Arnaud |
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Titolo |
Differential Equations and Population Dynamics I : Introductory Approaches / / by Arnaud Ducrot, Quentin Griette, Zhihua Liu, Pierre Magal |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 |
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ISBN |
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Edizione |
[1st ed. 2022.] |
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Descrizione fisica |
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1 online resource (466 pages) |
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Collana |
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Lecture Notes on Mathematical Modelling in the Life Sciences, , 2193-4797 |
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Disciplina |
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Soggetti |
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Mathematics |
Differential equations |
Epidemiology |
Mathematical models |
Applications of Mathematics |
Differential Equations |
Mathematical Modeling and Industrial Mathematics |
Models matemàtics |
Població |
Malalties infeccioses |
Equacions diferencials |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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 |
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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. |
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Sommario/riassunto |
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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. |
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