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Dynamical Systems and Their Applications in Biology
Edited by: Shigui Ruan, Dalhousie University, Halifax, NS, Canada, Gail S. K. Wolkowicz, McMaster University, Hamilton, ON, Canada, and Jianhong Wu, York University, North York, ON, Canada
A co-publication of the AMS and Fields Institute.

Fields Institute Communications
2003; 268 pp; hardcover
Volume: 36
ISBN-10: 0-8218-3163-1
ISBN-13: 978-0-8218-3163-2
List Price: US$87
Member Price: US$69.60
Order Code: FIC/36
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Differential Equations with Applications to Biology - Shigui Ruan, Gail S K Wolkowicz and Jianhong Wu

This volume is based on the proceedings of the International Workshop on Dynamical Systems and their Applications in Biology held at the Canadian Coast Guard College on Cape Breton Island (Nova Scotia, Canada). It presents a broad picture of the current research surrounding applications of dynamical systems in biology, particularly in population biology.

The book contains 19 papers and includes articles on the qualitative and/or numerical analysis of models involving ordinary, partial, functional, and stochastic differential equations. Applications include epidemiology, population dynamics, and physiology.

The material is suitable for graduate students and research mathematicians interested in ordinary differential equations and their applications in biology. Also available by Ruan, Wolkowicz, and Wu is Differential Equations with Applications to Biology, Volume 21 in the AMS series, Fields Institute Communications.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).


Graduate students and research mathematicians interested in ordinary differential equations and their applications.


"This volume is a highly selective and carefully edited piece ... a collection of well-written and balanced articles by ... well-known researchers at the interface of biomathematics and dynamical systems ... the work represents frontiers or emerging frontiers of biomathematics research."

-- SIAM Review

Table of Contents

  • J. Atamanyk and W. F. Langford -- A compartmental model of Cheyne-Stokes respiration
  • M. Bachar and O. Arino -- Integrated semigroup and linear ordinary differential equation with impulses
  • C. Bauch and D. J. D. Earn -- Interepidemic intervals in forced and unforced SEIR models
  • E. Beretta, H. Sakakibara, and Y. Takeuchi -- Stability analysis of time delayed chemostat models for bacteria and virulent phage
  • J. Best, C. Castillo-Chavez, and A.-A. Yakubu -- Hierarchical competition in discrete time models with dispersal
  • F. Brauer -- Stability and instability theorems for a characteristic equation arising in epidemic modeling
  • F. Brauer and P. van den Driessche -- Some directions for mathematical epidemiology
  • Y. Chen -- Global attractivity of a population model with state-dependent delay
  • Z. Feng, Y. Yi, and H. Zhu -- Metapopulation dynamics with migration and local competition
  • S. A. Gourley -- Oscillations and convergence in a harvesting model with sawtooth delay
  • W. Li and M. Zhang -- Rigidity for differentiable classification of one-dimensional dynamical systems
  • X. Liu -- Management of biological populations via impulsive control
  • C. C. McCluskey -- Stability for a class of three-dimensional homogeneous systems
  • I. Ncube, S. A. Campbell, and J. Wu -- Change in criticality of synchronous Hopf bifurcation in a multiple-delayed neural system
  • Y. Saito and Y. Takeuchi -- Sharp conditions for global stability of Lotka-Volterra systems with delayed intraspecific competitions
  • H. L. Smith and B. Li -- Competition for essential resources: A brief review
  • X. H. Tang, L. Wang, and X. Zou -- 3/2 type criteria for global attractivity of Lotka-Volterra discrete system with delays
  • P. van den Driessche and J. Watmough -- Epidemic solutions and endemic catastrophies
  • X.-Q. Zhao -- Persistence in almost periodic predator-prey reaction-diffusion systems
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