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Differential Equations with Applications to 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
1999; 509 pp; hardcover
Volume: 21
ISBN-10: 0-8218-0944-X
ISBN-13: 978-0-8218-0944-0
List Price: US$156
Member Price: US$124.80
Order Code: FIC/21
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Dynamical Systems and Their Applications in Biology - Shigui Ruan, Gail S K Wolkowicz and Jianhong Wu

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 Mathématiques, 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.


  • An overview of current developments in differential equations and mathematical biology.
  • Authoritative contributions from over 60 leading worldwide researchers.
  • Original, refereed contributions.

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


Graduate students, and research and applied mathematicians and scientists working in biology, ecology, epidemiology, neurobiology, and physiology.

Table of Contents

  • W. Allegretto and P. Nistri -- On a class of nonlocal problems with applications to mathematical biology
  • L. J. S. Allen, E. J. Allen, and D. N. Atkinson -- Integrodifference equations applied to plant dispersal, competition, and control
  • M. Benaïm and M. W. Hirsch -- Differential and stochastic epidemic models
  • F. Brauer -- General recruitment models for sexually transmitted diseases
  • J. R. Buchanan -- Asymptotic behavior of two interacting pioneer climax/species
  • S. A. Campbell -- Stability and bifurcation of a simple neural network with multiple time delays
  • D. Chao and S. A. Levin -- Herding behavior: The emergence of large-scale phenomena from local interactions
  • C. J. Clements, J. C. Clements, and B. M. Horáček -- On the formation of scroll waves in an anisotropic ventricular myocardium
  • J. C. Clements -- An optimal control theory approach to the inverse problem of electrocardiography
  • R. Cressman -- Natural selection as an extensive form game
  • L. Dung, H. L. Smith, and P. Waltman -- Growth in the unstirred chemostat with different diffusion rates
  • T. Faria -- Bifurcation aspects for some delayed population models with diffusion
  • J. E. Franke and A.-A. Yakubu -- Extinction and persistence in a size-structured, discrete competitive system with dispersion
  • H. I. Freedman and X.-Q. Zhao -- Global attractivity in a nonlocal reaction-diffusion model
  • P. Freitas -- Nonlocal reaction-diffusion equations
  • T. C. Gard -- Practical persistence in stochastic population models
  • T. Gedeon -- Stucture and dynamics of artificial neural networks
  • T. Gedeon and L. Glass -- Continuity of resetting curves for FitzHugh-Nagumo equations on the circle
  • L. Genik and P. van den Driessche -- An epidemic model with recruitment-death demographics and discrete delays
  • K. P. Hadeler -- Nonlinear propagation in reaction transport systems
  • U. an der Heiden -- On the dynamics of nonlinear feedback loops in cell membrane, neural and sensory systems
  • Y. Hino and S. Murikami -- Skew product flows of quasi-processes and stabilities
  • Y. S. Huang -- Periodic solutions to system of globally coupled oscillators
  • Y. Kan-on -- Bifurcation structure of stationary solutions of a Lotka-Volterra competition model with density-dependent diffusion
  • J. Kato and J. Pan -- Stability domain of a chemostat system with delay
  • Q. Kong -- Oscillation criteria for second order half-linear differential equations
  • Y. Kuang -- Rich dynamics of Gause-type ratio-dependent predator-prey system
  • L. A. C. Ladeira -- Differentiability with respect to delays for a neutral differential-difference equation
  • J. P. Lampreia, R. Severino, and J. Sousa Ramos -- Renormalizations for trimodal maps
  • A. Lasota and M. C. Mackey -- Statistical stability of strongly perturbed dynamical systems
  • X. Liu -- A generalization of variation of parameters and Lyapunov's method
  • J. Milota -- Persistence in an epidemiological model
  • Y. Morita, M. Pernarowski, and J. Dockery -- Homoclinic bifurcations in a diffusively coupled excitable system
  • H. Petzeltová -- Compactness and asymptotic spatial homogeneity in conservation laws with memory
  • K. Schmitt -- On boundary value problems for quasilinear elliptic equations
  • J. F. Selgrade and P. M. Schlosser -- A model for the production of ovarian hormones during the menstrual cycle
  • J. W.-H. So and J. S. Yu -- Global stability for a general population model with time delays
  • H. R. Thieme and P. van den Driessche -- Global stability in cyclic epidemic models with disease fatalities
  • B. Toni, D. Thieffry, and R. Bulajich -- Feedback loops analysis for chaotic dynamics with an application to Lorenz system
  • W. Wu and Z. Deng -- Absolute stability of the second canonical form of control systems
  • D. Xiao and S. Ruan -- Bogdanov-Takens bifurcations in predator-prey systems with constant rate harvesting
  • List of participants
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