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Differential Equations and Population Dynamics I
Introductory Approaches, Lecture Notes on Mathematical Modelling in the Life Sciences
Ducrot, Arnaud/Griette, Quentin/Liu, Zhihua et al
ISBN/EAN: 9783030981358
Umbreit-Nr.: 5128393
Sprache:
Englisch
Umfang: xx, 458 S.
Format in cm:
Einband:
kartoniertes Buch
Erschienen am 21.06.2022
Auflage: 1/2022
- Zusatztext
- This book presents the basic theoretical concepts of dynamical systems with applications in population dynamics. Existence, uniqueness and stability of solutions, global attractors, bifurcations, center manifold and normal form theories are discussed with cutting-edge applications, including a Holling's predator-prey model with handling and searching predators and projecting the epidemic forward with varying level of public health interventions for COVID-19.As an interdisciplinary text, this book aims at bridging the gap between mathematics, biology and medicine by integrating relevant concepts from these subject areas, making it self-sufficient for the reader. It will be a valuable resource to graduate and advance undergraduate students for interdisciplinary research in the area of mathematics and population dynamics.
- Kurztext
- 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.
- Autorenportrait
- Arnaud Ducrot is professor of mathematics at the University Le Havre Normandie, France. His research interests include analysis, dynamical systems and mathematical aspects of population dynamics and the natural sciences. Quentin Griette is an associate professor in mathematics at the University of Bordeaux, France. His areas of expertise include ordinary differential equations, reaction-diffusion systems and the numerical computation of their solutions. Zhihua Liu is a professor of mathematics at Beijing Normal University, China. Her research interests include differential equations, dynamical systems and applications in epidemics and population dynamics. Pierre Magal is professor of mathematics at the University of Bordeaux, France. His research interests include differential equations, dynamical systems, numerical simulations and mathematical biology.