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Differential Equations with Applications to Biology
     

Differential Equations with Applications to Biology

by Shigui Ruan, Gail S. Wolkowicz, Jianhong Wu, Gail S. K. Wolkowicz
 

ISBN-10: 082180944X

ISBN-13: 9780821809440

Pub. Date: 10/26/1998

Publisher: American Mathematical Society

This book presents the proceedings from the International Conference held in Halifax, NS in July 1997. Funded by The Fields Institute and Le Centre de Recherches Mathematiques, the conference was held in honor of the retirement of Professors Lynn Erbe and Herb I. Freedman (University of Alberta). Featured topics include ordinary, partial, functional, and stochastic

Overview

This book presents the proceedings from the International Conference held in Halifax, NS in July 1997. Funded by The Fields Institute and Le Centre de Recherches Mathematiques, the conference was held in honor of the retirement of Professors Lynn Erbe and Herb I. Freedman (University of Alberta). Featured topics include ordinary, partial, functional, and stochastic differential equations and their applications to biology, epidemiology, neurobiology, physiology and other related areas. The 41 papers included in this volume represent the recent work of leading researchers over a wide range of subjects, including bifurcation theory, chaos, stability theory, boundary value problems, persistence theory, neural networks, disease transmission, population dynamics, pattern formation and more. The text would be suitable for a graduate or advanced undergraduate course study in mathematical biology. Features: An overview of current developments in differential equations and mathematical biology. Authoritative contributions from over 60 leading worldwide researchers. Original, refereed contributions.

Product Details

ISBN-13:
9780821809440
Publisher:
American Mathematical Society
Publication date:
10/26/1998
Series:
Fields Institute Communications Series , #21
Pages:
509
Product dimensions:
7.48(w) x 10.63(h) x (d)

Table of Contents

Prefaceix
On a Class of Nonlocal Problems with Applications to Mathematical Biology1
Integrodifference Equations Applied to Plant Dispersal, Competition, and Control15
Differential and Stochastic Epidemic Models31
General Recruitment Models for Sexually Transmitted Diseases45
Asymptotic Behavior of Two Interacting Pioneer/Climax Species51
Stability and Bifurcation of a Simple Neural Network with Multiple Time Delays65
Herding Behavior: The Emergence of Large-Scale Phenomena from Local Interactions81
On the Formation of Scroll Waves in an Anisotropic Ventricular Myocardium97
An Optimal Control Theory Approach to the Inverse Problem of Electrocardiography109
Natural Selection as an Extensive Form Game119
Growth in the Unstirred Chemostat with Different Diffusion Rates131
Bifurcation Aspects for some Delayed Population Models with Diffusion143
Extinction and Persistence in a Size-Structured, Discrete Competitive System with Dispersion159
Global Attractivity in a Nonlocal Reaction-Diffusion Model175
Nonlocal Reaction-Diffusion Equations187
Practical Persistence in Stochastic Population Models205
Structure and Dynamics of Artifical Neural Networks217
Continuity of Resetting Curves for FitzHugh-Nagumo Equations on the Circle225
An Epidemic Model with Recruitment-Death Demographics and Discrete Delays237
Nonlinear Propagation in Reaction Transport Systems251
On the Dynamics of Nonlinear Feedback Loops in Cell Membrane, Neural and Sensory Systems259
Skew Product Flows of Quasi-Processes and Stabilities269
Periodic Solutions to System of Globally Coupled Oscillators279
Bifurcation Structure of Stationary Solutions of a Lotka-Volterra Competition Model with Density-Dependent Diffusion293
Stability Domain of a Chemostat System with Delay307
Oscillation Criteria for Second Order Half-Linear Differential Equations317
Rich Dynamics of Gause-Type Ratio-Dependent Predator-Prey System325
Differentiability with Respect to Delays for a Neutral Differential-Difference Equation339
Renormalizations for Trimodal Maps353
Statistical Stability of Strongly Perturbed Dynamical Systems363
A Generalization of Variation of Parameters and Lyapunov's Method377
Persistence in an Epidemiological Model387
Homoclinic Bifurcations in a Diffusively Coupled Excitable System397
Compactness and Asymptotic Spatial Homogeneity in Conservation Laws with Memory409
On Boundary Value Problems for Quasilinear Elliptic Equations419
A Model for the Production of Ovarian Hormones during the Menstrual Cycle429
Global Stability for a General Population Model with Time Delays447
Global Stability in Cyclic Epidemic Models with Disease Fatalities459
Feedback Loops Analysis for Chaotic Dynamics with an Application to Lorenz System473
Absolute Stability of the Second Canonical Form of Control Systems485
Bogdanov-Takens Bifurcations in Predator-Prey Systems with Constant Rate Harvesting493
AppendixList of Participants507

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