Shigui Ruan's Books

Differential Equations with Applications to Biology

By: Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu

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Differential Equations with Applications to Biology

By: Shigui Ruan,Gail Susan Kohl Wolkowicz,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. Features: An overview of current developments in differential equations and mathematical biology. Authoritative contributions from over 60 leading worldwide researchers. Original, refereed contributions.

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Page Count

521

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082180944X

ISBN 13

9780821809440

Dynamical Systems and Their Applications in Biology

By: Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu

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Dynamical Systems and Their Applications in Biology

By: Shigui Ruan,Gail Susan Kohl Wolkowicz,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.

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Page Count

280

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821831631

ISBN 13

9780821831632

Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models

By: Pierre Magal,Shigui Ruan

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Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models

By: Pierre Magal,Shigui Ruan

Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using Liapunov-Perron method and following the techniques of Vanderbauwhede et al. in treating infinite dimensional systems, the authors study the existence and smoothness of center manifolds for semilinear Cauchy problems with non-dense domain. As an application, they use the center manifold theorem to establish a Hopf bifurcation theorem for age structured models.

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American Mathematical Soc.

Published Date

ISBN 10

0821846531

ISBN 13

9780821846537

Theory and Applications of Abstract Semilinear Cauchy Problems

By: Pierre Magal,Shigui Ruan

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Theory and Applications of Abstract Semilinear Cauchy Problems

By: Pierre Magal,Shigui Ruan

Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems.

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