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.
Table of Contents:
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.
About the Author :
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.
