Stability and Oscillations in Delay Differential Equations of Population Dynamics / Edition 1

by K. Gopalsamy

Overview

This monograph provides a definitive overview of recent advances in the stability and oscillation of autonomous delay differential equations. Topics include linear and nonlinear delay and integrodifferential equations, which have potential applications to both biological and physical dynamic processes.
Chapter 1 deals with an analysis of the dynamical characteristics of the delay logistic equation, and a number of techniques and results relating to stability, oscillation and comparison of scalar delay and integrodifferential equations are presented. Chapter 2 provides a tutorial-style introduction to the study of delay-induced Hopf bifurcation to periodicity and the related computations for the analysis of the stability of bifurcating periodic solutions. Chapter 3 is devoted to local analyses of nonlinear model systems and discusses many methods applicable to linear equations and their perturbations. Chapter 4 considers global convergence to equilibrium states of nonlinear systems, and includes oscillations of nonlinear systems about their equilibria. Qualitative analyses of both competitive and cooperative systems with time delays feature in both Chapters 3 and 4. Finally, Chapter 5 deals with recent developments in models of neutral differential equations and their applications to population dynamics. Each chapter concludes with a number of exercises and the overall exposition recommends this volume as a good supplementary text for graduate courses.
For mathematicians whose work involves functional differential equations, and whose interest extends beyond the boundaries of linear stability analysis.

Product Details

ISBN-13:	9789048141197
Publisher:	Springer Netherlands
Publication date:	12/08/2010
Series:	Mathematics and Its Applications , #74
Edition description:	Softcover reprint of hardcover 1st ed. 1992
Pages:	502
Product dimensions:	6.30(w) x 9.45(h) x 0.04(d)

Table of Contents

1. The Delay Logistic Equation.- 2. Delay Induced Bifurcation to Periodicity.- 3. Methods of Linear Analysis.- 4. Global Attractivity.- 5. Models of Neutral Differential Systems.- References.