Delay Differential Equations

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An Introduction to Delay Differential Equations with Applications to the Life Sciences

hal smith
An Introduction to Delay Differential Equations with Applications to the Life Sciences Book PDF

Author : hal smith
Publisher : Springer Science & Business Media
Page : 178 pages
File Size : 53,7 Mb
Release : 2010-09-29
Category : Mathematics
ISBN : 9781441976468

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An Introduction to Delay Differential Equations with Applications to the Life Sciences by hal smith Pdf

This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a reasonable background in ordinary differential equations and who would like to get to the applications quickly. The author has used preliminary notes in teaching such a course at Arizona State University over the past two years. This book focuses on the key tools necessary to understand the applications literature involving delay equations and to construct and analyze mathematical models involving delay differential equations. The book begins with a survey of mathematical models involving delay equations.

Ordinary and Delay Differential Equations

R. D. Driver
Ordinary and Delay Differential Equations Book PDF

Author : R. D. Driver
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468494679

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Ordinary and Delay Differential Equations by R. D. Driver Pdf

This textbook is designed for the intermediate-level course on ordinary differential equations offered at many universities and colleges. It treats, as standard topics of such a course: existence and uniqueness theory, linear s- terns, stability theory, and introductory phase-plane analysis of autonomous second order systems. The unique feature of the book is its further inc- sion of a substantial introduction to delay differential eq- tions. Such equations are motivated by problems in control theory, physics, biology, ecology, economics, inventory c- trol, and the theory of nuclear reactors. The surge of interest in delay differential equations during the past two or three decades is evidenced by th- sands of research papers on the subject and about 20 published books devoted in whole or in part to these equations. The v * ... books include those of Myskis [1951], El' sgol' c [1955] and [1964], Pinney [1958], Krasovskil [1959], Bellman and Cooke [1963], Norkin [1965], Halanay [1966], Oguztoreli [1966], Lakshmikantham and Leela [1969], Mitropol'skir and Martynjuk [1969], Martynjuk [1971], and Hale [1971], plus a number of symposium and seminar proceedings published in the U.S. and the U.S.S.R. These books have influenced the present textbook.

Delay Equations

Odo Diekmann,Stephan A.van Gils,Sjoerd M.V. Lunel,Hans-Otto Walther
Delay Equations Book PDF

Author : Odo Diekmann,Stephan A.van Gils,Sjoerd M.V. Lunel,Hans-Otto Walther
Publisher : Springer Science & Business Media
Page : 547 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242062

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Delay Equations by Odo Diekmann,Stephan A.van Gils,Sjoerd M.V. Lunel,Hans-Otto Walther Pdf

The aim here is to provide an introduction to the mathematical theory of infinite dimensional dynamical systems by focusing on a relatively simple - yet rich - class of examples, delay differential equations. This textbook contains detailed proofs and many exercises, intended both for self-study and for courses at graduate level, as well as a reference for basic results. As the subtitle indicates, this book is about concepts, ideas, results and methods from linear functional analysis, complex function theory, the qualitative theory of dynamical systems and nonlinear analysis. The book provides the reader with a working knowledge of applied functional analysis and dynamical systems.

Applied Delay Differential Equations

Thomas Erneux
Applied Delay Differential Equations Book PDF

Author : Thomas Erneux
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 49,7 Mb
Release : 2009-03-06
Category : Mathematics
ISBN : 9780387743721

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Applied Delay Differential Equations by Thomas Erneux Pdf

Applied Delay Differential Equations is a friendly introduction to the fast-growing field of time-delay differential equations. Written to a multi-disciplinary audience, it sets each area of science in his historical context and then guides the reader towards questions of current interest.

Delay Differential Equations and Applications to Biology

Fathalla A. Rihan
Delay Differential Equations and Applications to Biology Book PDF

Author : Fathalla A. Rihan
Publisher : Springer Nature
Page : 292 pages
File Size : 44,8 Mb
Release : 2021-08-19
Category : Mathematics
ISBN : 9789811606267

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Delay Differential Equations and Applications to Biology by Fathalla A. Rihan Pdf

This book discusses the numerical treatment of delay differential equations and their applications in bioscience. A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems. The book also provides interesting applications of delay differential equations in infectious diseases, including COVID-19. It will be valuable to mathematicians and specialists associated with mathematical biology, mathematical modelling, life sciences, immunology and infectious diseases.

Stability and Oscillations in Delay Differential Equations of Population Dynamics

K. Gopalsamy
Stability and Oscillations in Delay Differential Equations of Population Dynamics Book PDF

Author : K. Gopalsamy
Publisher : Springer Science & Business Media
Page : 514 pages
File Size : 40,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401579209

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Stability and Oscillations in Delay Differential Equations of Population Dynamics by K. Gopalsamy Pdf

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.

Stability of Linear Delay Differential Equations

Dimitri Breda,Stefano Maset,Rossana Vermiglio
Stability of Linear Delay Differential Equations Book PDF

Author : Dimitri Breda,Stefano Maset,Rossana Vermiglio
Publisher : Springer
Page : 158 pages
File Size : 52,6 Mb
Release : 2014-10-21
Category : Science
ISBN : 9781493921072

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Stability of Linear Delay Differential Equations by Dimitri Breda,Stefano Maset,Rossana Vermiglio Pdf

This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a complete and self-contained treatment, which includes the basic underlying mathematics and numerics, examples from population dynamics and engineering applications, and Matlab programs implementing the proposed numerical methods. A number of proofs is given to furnish a solid foundation, but the emphasis is on the (unifying) idea of the pseudospectral technique for the stability analysis of DDEs. It is aimed at advanced students and researchers in applied mathematics, in dynamical systems and in various fields of science and engineering, concerned with delay systems. A relevant feature of the book is that it also provides the Matlab codes to encourage the readers to experience the practical aspects. They could use the codes to test the theory and to analyze the performances of the methods on the given examples. Moreover, they could easily modify them to tackle the numerical stability analysis of their own delay models.

Delay Differential Equations and Applications

O. Arino,M.L. Hbid,E. Ait Dads
Delay Differential Equations and Applications Book PDF

Author : O. Arino,M.L. Hbid,E. Ait Dads
Publisher : Springer Science & Business Media
Page : 612 pages
File Size : 50,8 Mb
Release : 2006-09-25
Category : Mathematics
ISBN : 1402036469

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Delay Differential Equations and Applications by O. Arino,M.L. Hbid,E. Ait Dads Pdf

This book groups material that was used for the Marrakech 2002 School on Delay Di'erential Equations and Applications. The school was held from September 9-21 2002 at the Semlalia College of Sciences of the Cadi Ayyad University, Marrakech, Morocco. 47 participants and 15 instructors originating from 21 countries attended the school. Fin- cial limitations only allowed support for part of the people from Africa andAsiawhohadexpressedtheirinterestintheschoolandhadhopedto come. Theschoolwassupportedby'nancementsfromNATO-ASI(Nato advanced School), the International Centre of Pure and Applied Mat- matics (CIMPA, Nice, France) and Cadi Ayyad University. The activity of the school consisted in courses, plenary lectures (3) and communi- tions (9), from Monday through Friday, 8. 30 am to 6. 30 pm. Courses were divided into units of 45mn duration, taught by block of two units, with a short 5mn break between two units within a block, and a 25mn break between two blocks. The school was intended for mathematicians willing to acquire some familiarity with delay di'erential equations or enhance their knowledge on this subject. The aim was indeed to extend the basic set of knowledge, including ordinary di'erential equations and semilinearevolutionequations,suchasforexamplethedi'usion-reaction equations arising in morphogenesis or the Belouzov-Zhabotinsky ch- ical reaction, and the classic approach for the resolution of these eq- tions by perturbation, to equations having in addition terms involving past values of the solution.

Functional Differential Equations with Infinite Delay

Yoshiyuki Hino,Satoru Murakami,Toshiki Naito
Functional Differential Equations with Infinite Delay Book PDF

Author : Yoshiyuki Hino,Satoru Murakami,Toshiki Naito
Publisher : Springer
Page : 326 pages
File Size : 50,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540473886

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Functional Differential Equations with Infinite Delay by Yoshiyuki Hino,Satoru Murakami,Toshiki Naito Pdf

In the theory of functional differential equations with infinite delay, there are several ways to choose the space of initial functions (phase space); and diverse (duplicated) theories arise, according to the choice of phase space. To unify the theories, an axiomatic approach has been taken since the 1960's. This book is intended as a guide for the axiomatic approach to the theory of equations with infinite delay and a culmination of the results obtained in this way. It can also be used as a textbook for a graduate course. The prerequisite knowledge is foundations of analysis including linear algebra and functional analysis. It is hoped that the book will prepare students for further study of this area, and that will serve as a ready reference to the researchers in applied analysis and engineering sciences.

Delay Differential Equations

Yang Kuang
Delay Differential Equations Book PDF

Author : Yang Kuang
Publisher : Academic Press
Page : 398 pages
File Size : 46,5 Mb
Release : 1993-03-05
Category : Mathematics
ISBN : 0080960022

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Delay Differential Equations by Yang Kuang Pdf

Delay Differential Equations emphasizes the global analysis of full nonlinear equations or systems. The book treats both autonomous and nonautonomous systems with various delays. Key topics addressed are the possible delay influence on the dynamics of the system, such as stability switching as time delay increases, the long time coexistence of populations, and the oscillatory aspects of the dynamics. The book also includes coverage of the interplay of spatial diffusion and time delays in some diffusive delay population models. The treatment presented in this monograph will be of great value in the study of various classes of DDEs and their multidisciplinary applications.

Numerical Methods for Delay Differential Equations

Alfredo Bellen,Marino Zennaro
Numerical Methods for Delay Differential Equations Book PDF

Author : Alfredo Bellen,Marino Zennaro
Publisher : Numerical Mathematics and Scie
Page : 411 pages
File Size : 51,7 Mb
Release : 2013-01-10
Category : Business & Economics
ISBN : 9780199671373

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Numerical Methods for Delay Differential Equations by Alfredo Bellen,Marino Zennaro Pdf

This unique book describes, analyses, and improves various approaches and techniques for the numerical solution of delay differential equations. It includes a list of available codes and also aids the reader in writing his or her own.

Delay and Functional Differential Equations and Their Applications

Klaus Schmitt
Delay and Functional Differential Equations and Their Applications Book PDF

Author : Klaus Schmitt
Publisher : Elsevier
Page : 412 pages
File Size : 44,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483272337

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Delay and Functional Differential Equations and Their Applications by Klaus Schmitt Pdf

Delay and Functional Differential Equations and Their Applications provides information pertinent to the fundamental aspects of functional differential equations and its applications. This book covers a variety of topics, including qualitative and geometric theory, control theory, Volterra equations, numerical methods, the theory of epidemics, problems in physiology, and other areas of applications. Organized into two parts encompassing 25 chapters, this book begins with an overview of problems involving functional differential equations with terminal conditions in function spaces. This text then examines the numerical methods for functional differential equations. Other chapters consider the theory of radiative transfer, which give rise to several interesting functional partial differential equations. This book discusses as well the theory of embedding fields, which studies systems of nonlinear functional differential equations that can be derived from psychological postulates and interpreted as neural networks. The final chapter deals with the usefulness of the flip-flop circuit. This book is a valuable resource for mathematicians.

Oscillation Theory of Delay Differential Equations

I. Győri,G. E. Ladas
Oscillation Theory of Delay Differential Equations Book PDF

Author : I. Győri,G. E. Ladas
Publisher : Clarendon Press
Page : 392 pages
File Size : 53,6 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015025010995

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Oscillation Theory of Delay Differential Equations by I. Győri,G. E. Ladas Pdf

In recent years there has been a resurgence of interest in the study of delay differential equations motivated largely by new applications in physics, biology, ecology, and physiology. The aim of this monograph is to present a reasonably self-contained account of the advances in the oscillation theory of this class of equations. Throughout, the main topics of study are shown in action, with applications to such diverse problems as insect population estimations, logistic equations in ecology, the survival of red blood cells in animals, integro-differential equations, and the motion of the tips of growing plants. The authors begin by reviewing the basic theory of delay differential equations, including the fundamental results of existence and uniqueness of solutions and the theory of the Laplace and z-transforms. Little prior knowledge of the subject is required other than a firm grounding in the main techniques of differential equation theory. As a result, this book provides an invaluable reference to the recent work both for mathematicians and for all those whose research includes the study of this fascinating class of differential equations.

Oscillation Theory for Neutral Differential Equations with Delay

D.D Bainov,D.P Mishev
Oscillation Theory for Neutral Differential Equations with Delay Book PDF

Author : D.D Bainov,D.P Mishev
Publisher : CRC Press
Page : 296 pages
File Size : 46,9 Mb
Release : 1991-01-01
Category : Mathematics
ISBN : 0750301422

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Oscillation Theory for Neutral Differential Equations with Delay by D.D Bainov,D.P Mishev Pdf

With neutral differential equations, any lack of smoothness in initial conditions is not damped and so they have proven to be difficult to solve. Until now, there has been little information to help with this problem. Oscillation Theory for Neutral Differential Equations with Delay fills a vacuum in qualitative theory of functional differential equations of neutral type. With much of the presented material previously unavailable outside Eastern Europe, this authoritative book provides a stimulus to research the oscillatory and asymptotic properties of these equations. It examines equations of first, second, and higher orders as well as the asymptotic behavior for tending toward infinity. These results are then generalized for partial differential equations of neutral type. The book also describes the historical development of the field and discusses applications in mathematical models of processes and phenomena in physics, electrical control and engineering, physical chemistry, and mathematical biology. This book is an important tool not only for mathematicians, but also for specialists in many fields including physicists, engineers, and biologists. It may be used as a graduate-level textbook or as a reference book for a wide range of subjects, from radiophysics to electrical and control engineering to biological science.

Numerical Continuation Methods for Dynamical Systems

Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque
Numerical Continuation Methods for Dynamical Systems Book PDF

Author : Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque
Publisher : Springer
Page : 399 pages
File Size : 50,6 Mb
Release : 2007-11-06
Category : Science
ISBN : 9781402063565

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Numerical Continuation Methods for Dynamical Systems by Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque Pdf

Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.