Differential equations and population dynamics II advanced approaches Arnaud Ducrot, Quentin Griette, Zhihua Liu, Pierre Magal

Format:

Book

Author/Creator:

Ducrot, Arnaud, author.

Griette, Quentin, author.

Liu, Zhihua, author.

Magal, Pierre, author.

Series:

Lecture notes on mathematical modelling in the life sciences 2193-4797

Language:

English

Subjects (All):

Population--Mathematical models.

Population.

Differential equations.

Physical Description:

1 online resource

Other Title:

Differential equations and population dynamics 2

Place of Publication:

Cham Springer [2026]

Summary:

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

Contents:

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

Notes:

Includes bibliographical references

Online resource; title from PDF title page (SpringerLink, viewed May 4, 2026)

Other Format:

Print version Ducrot, Arnaud Differential Equations and Population Dynamics II

ISBN:

9783031914096

3031914090

OCLC:

1588215127

Access Restriction:

Restricted for use by site license