Topics in mathematical biology:
This book analyzes the impact of quiescent phases on biological models. Quiescence arises, for example, when moving individuals stop moving, hunting predators take a rest, infected individuals are isolated, or cells enter the quiescent compartment of the cell cycle. In the first chapter of Topics in...
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer Nature
[2017]
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| Schriftenreihe: | Lecture notes on mathematical modelling in the life sciences
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| Schlagworte: | |
| Online-Zugang: | Inhaltstext |
| Zusammenfassung: | This book analyzes the impact of quiescent phases on biological models. Quiescence arises, for example, when moving individuals stop moving, hunting predators take a rest, infected individuals are isolated, or cells enter the quiescent compartment of the cell cycle. In the first chapter of Topics in Mathematical Biology general principles about coupled and quiescent systems are derived, including results on shrinking periodic orbits and stabilization of oscillations via quiescence. In subsequent chapters classical biological models are presented in detail and challenged by the introduction of quiescence. These models include delay equations, demographic models, age structured models, Lotka-Volterra systems, replicator systems, genetic models, game theory, Nash equilibria, evolutionary stable strategies, ecological models, epidemiological models, random walks and reaction-diffusion models. In each case we find new and interesting results such as stability of fixed points and/or periodic orbits, excitability of steady states, epidemic outbreaks, survival of the fittest, and speeds of invading fronts. The textbook is intended for graduate students and researchers in mathematical biology who have a solid background in linear algebra, differential equations and dynamical systems. Readers can find gems of unexpected beauty within these pages, and those who knew K.P. (as he was often called) well will likely feel his presence and hear him speaking to them as they read Preface -- 1.Coupling and quiescence -- 2.Delay and age -- 3.Lotka-Volterra and replicator systems -- 4.Ecology -- 5.Homogeneous systems -- 6.Epidemic models -- 7.Coupled movements -- 8.Traveling fronts -- Index |
| Beschreibung: | xiv, 353 Seiten Diagramme |
| ISBN: | 9783319656205 |
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| 520 | 3 | |a This book analyzes the impact of quiescent phases on biological models. Quiescence arises, for example, when moving individuals stop moving, hunting predators take a rest, infected individuals are isolated, or cells enter the quiescent compartment of the cell cycle. In the first chapter of Topics in Mathematical Biology general principles about coupled and quiescent systems are derived, including results on shrinking periodic orbits and stabilization of oscillations via quiescence. In subsequent chapters classical biological models are presented in detail and challenged by the introduction of quiescence. These models include delay equations, demographic models, age structured models, Lotka-Volterra systems, replicator systems, genetic models, game theory, Nash equilibria, evolutionary stable strategies, ecological models, epidemiological models, random walks and reaction-diffusion models. In each case we find new and interesting results such as stability of fixed points and/or periodic orbits, excitability of steady states, epidemic outbreaks, survival of the fittest, and speeds of invading fronts. The textbook is intended for graduate students and researchers in mathematical biology who have a solid background in linear algebra, differential equations and dynamical systems. Readers can find gems of unexpected beauty within these pages, and those who knew K.P. (as he was often called) well will likely feel his presence and hear him speaking to them as they read | |
| 520 | 3 | |a Preface -- 1.Coupling and quiescence -- 2.Delay and age -- 3.Lotka-Volterra and replicator systems -- 4.Ecology -- 5.Homogeneous systems -- 6.Epidemic models -- 7.Coupled movements -- 8.Traveling fronts -- Index | |
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Datensatz im Suchindex
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| discipline | Biologie |
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| id | DE-604.BV046622340 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T14:08:32Z |
| indexdate | 2024-12-09T13:05:04Z |
| institution | BVB |
| institution_GND | (DE-588)1065168780 |
| isbn | 9783319656205 |
| language | English |
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| physical | xiv, 353 Seiten Diagramme |
| publishDate | 2017 |
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| publisher | Springer Nature |
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| series2 | Lecture notes on mathematical modelling in the life sciences |
| spelling | Hadeler, Karl-Peter 1936-2017 (DE-588)107953366 aut Topics in mathematical biology Karl Peter Hadeler Cham Springer Nature [2017] xiv, 353 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes on mathematical modelling in the life sciences This book analyzes the impact of quiescent phases on biological models. Quiescence arises, for example, when moving individuals stop moving, hunting predators take a rest, infected individuals are isolated, or cells enter the quiescent compartment of the cell cycle. In the first chapter of Topics in Mathematical Biology general principles about coupled and quiescent systems are derived, including results on shrinking periodic orbits and stabilization of oscillations via quiescence. In subsequent chapters classical biological models are presented in detail and challenged by the introduction of quiescence. These models include delay equations, demographic models, age structured models, Lotka-Volterra systems, replicator systems, genetic models, game theory, Nash equilibria, evolutionary stable strategies, ecological models, epidemiological models, random walks and reaction-diffusion models. In each case we find new and interesting results such as stability of fixed points and/or periodic orbits, excitability of steady states, epidemic outbreaks, survival of the fittest, and speeds of invading fronts. The textbook is intended for graduate students and researchers in mathematical biology who have a solid background in linear algebra, differential equations and dynamical systems. Readers can find gems of unexpected beauty within these pages, and those who knew K.P. (as he was often called) well will likely feel his presence and hear him speaking to them as they read Preface -- 1.Coupling and quiescence -- 2.Delay and age -- 3.Lotka-Volterra and replicator systems -- 4.Ecology -- 5.Homogeneous systems -- 6.Epidemic models -- 7.Coupled movements -- 8.Traveling fronts -- Index Mathematics Biomathematics Springer-Verlag GmbH (DE-588)1065168780 pbl Erscheint auch als Online-Ausgabe 10.1007/978-3-319-65621-2 B:ZBM V:DE-601 pdf/application http://zbmath.org/?q=an:1382.92003 2018-04-25 Verlag Zentralblatt MATH Inhaltstext |
| spellingShingle | Hadeler, Karl-Peter 1936-2017 Topics in mathematical biology |
| title | Topics in mathematical biology |
| title_auth | Topics in mathematical biology |
| title_exact_search | Topics in mathematical biology |
| title_exact_search_txtP | Topics in mathematical biology |
| title_full | Topics in mathematical biology Karl Peter Hadeler |
| title_fullStr | Topics in mathematical biology Karl Peter Hadeler |
| title_full_unstemmed | Topics in mathematical biology Karl Peter Hadeler |
| title_short | Topics in mathematical biology |
| title_sort | topics in mathematical biology |
| url | http://zbmath.org/?q=an:1382.92003 |
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