Differential Equations and Population Dynamics II : Advanced Approaches.DE (Lecture Notes on Mathematical Modelling in the Life Sciences)

Ducrot, Arnaud/ Griette, Quentin/ Liu, Zhihua

Springer, Berlin; Springer（2026発売）

Springer, Berlin; Springer（2026発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 472 p.
• 商品コード 9783031914119

Description

This book is the second volume in a two-part series on the theory of ordinary differential equations and their applications to population dynamics. 

While the first volume provides an introduction to the topic, this second volume presents advanced mathematical tools for analyzing such problems. 

Part I focuses on refined techniques for describing the long-term behavior of these systems. It includes a detailed discussion of dissipative dynamical systems, omega and alpha limit sets, global attractors, bifurcations, the construction of smooth center manifolds, and normal form theory. 

Part II introduces new perspectives on predator-prey systems by applying theoretical results to derive oscillating solutions through Hopf bifurcation, traveling invasion waves using global attractor theory, and a description of long-term dynamics in competitive interactions between predator variants. 

Throughout the book, concepts are illustrated with numerical examples, and MATLAB codes are provided. 

Bridging an interdisciplinary gap, this book will be valuable to graduate students and researchers studying mathematical models in population dynamics.

Part I Dynamical Systems in Population Dynamics.- 1 Semiflows, -limit Sets, -limit Sets, Attraction, and Dissipation.- 2 Global Attractors and Uniform Persistence.- 3 Bifurcations.- 4 Center Manifold and Center Unstable Manifold Theory.- 5 Normal Forms.- Part II Applications to Predator Prey Systems.- 6 A Holling s predator-prey model with handling and searching predators.- 7 Hopf bifurcation for a Holling s predator-prey model with handling and searching predators.- 8 Large Speed Traveling Waves for the Rosenzweig-MacArthur model.- 9 A predator-prey model with infinitely many variants.

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 natural sciences.

Quentin Griette is Professor of Mathematics at the University Le Havre Normandie, France. His research interests include ordinary differential equations, reaction-diffusion systems and the numerical computation of their solutions.

Zhihua Liu is 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 was Professor of Mathematics at the University of Bordeaux, France. His research interests included differential equations, dynamical systems, numerical simulations and mathematical biology.