On The Stability Of A Differential Delay Equation

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Stability of Linear Delay Differential Equations

Author : Dimitri Breda
Publisher : Springer
ISBN 13 : 149392107X
Total Pages : 162 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Stability of Linear Delay Differential Equations by : Dimitri Breda

Download or read book Stability of Linear Delay Differential Equations written by Dimitri Breda and published by Springer. This book was released on 2014-10-21 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stability and Oscillations in Delay Differential Equations of Population Dynamics

Author : K. Gopalsamy
Publisher : Springer Science & Business Media
ISBN 13 : 9780792315940
Total Pages : 526 pages
Book Rating : 4.3/5 (159 download)

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Book Synopsis Stability and Oscillations in Delay Differential Equations of Population Dynamics by : K. Gopalsamy

Download or read book Stability and Oscillations in Delay Differential Equations of Population Dynamics written by K. Gopalsamy and published by Springer Science & Business Media. This book was released on 1992-03-31 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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

Author : hal smith
Publisher : Springer Science & Business Media
ISBN 13 : 1441976469
Total Pages : 178 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis An Introduction to Delay Differential Equations with Applications to the Life Sciences by : hal smith

Download or read book An Introduction to Delay Differential Equations with Applications to the Life Sciences written by hal smith and published by Springer Science & Business Media. This book was released on 2010-09-29 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stability of Vector Differential Delay Equations

Author : Michael I. Gil’
Publisher : Springer Science & Business Media
ISBN 13 : 3034805772
Total Pages : 267 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Stability of Vector Differential Delay Equations by : Michael I. Gil’

Download or read book Stability of Vector Differential Delay Equations written by Michael I. Gil’ and published by Springer Science & Business Media. This book was released on 2013-02-14 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations with delay naturally arise in various applications, such as control systems, viscoelasticity, mechanics, nuclear reactors, distributed networks, heat flows, neural networks, combustion, interaction of species, microbiology, learning models, epidemiology, physiology, and many others. This book systematically investigates the stability of linear as well as nonlinear vector differential equations with delay and equations with causal mappings. It presents explicit conditions for exponential, absolute and input-to-state stabilities. These stability conditions are mainly formulated in terms of the determinants and eigenvalues of auxiliary matrices dependent on a parameter; the suggested approach allows us to apply the well-known results of the theory of matrices. In addition, solution estimates for the considered equations are established which provide the bounds for regions of attraction of steady states. The main methodology presented in the book is based on a combined usage of the recent norm estimates for matrix-valued functions and the following methods and results: the generalized Bohl-Perron principle and the integral version of the generalized Bohl-Perron principle; the freezing method; the positivity of fundamental solutions. A significant part of the book is devoted to the Aizerman-Myshkis problem and generalized Hill theory of periodic systems. The book is intended not only for specialists in the theory of functional differential equations and control theory, but also for anyone with a sound mathematical background interested in their various applications.

Functional Differential Equations with Infinite Delay

Author : Yoshiyuki Hino
Publisher : Springer
ISBN 13 : 3540473882
Total Pages : 326 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Functional Differential Equations with Infinite Delay by : Yoshiyuki Hino

Download or read book Functional Differential Equations with Infinite Delay written by Yoshiyuki Hino and published by Springer. This book was released on 2006-11-14 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Methods for Delay Differential Equations

Author : Alfredo Bellen
Publisher : Numerical Mathematics and Scie
ISBN 13 : 0199671370
Total Pages : 411 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis Numerical Methods for Delay Differential Equations by : Alfredo Bellen

Download or read book Numerical Methods for Delay Differential Equations written by Alfredo Bellen and published by Numerical Mathematics and Scie. This book was released on 2013-01-10 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Differential Equations and Applications to Biology

Author : Fathalla A. Rihan
Publisher : Springer Nature
ISBN 13 : 9811606269
Total Pages : 292 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Delay Differential Equations and Applications to Biology by : Fathalla A. Rihan

Download or read book Delay Differential Equations and Applications to Biology written by Fathalla A. Rihan and published by Springer Nature. This book was released on 2021-08-19 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applied Delay Differential Equations

Author : Thomas Erneux
Publisher : Springer Science & Business Media
ISBN 13 : 0387743723
Total Pages : 204 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Applied Delay Differential Equations by : Thomas Erneux

Download or read book Applied Delay Differential Equations written by Thomas Erneux and published by Springer Science & Business Media. This book was released on 2009-03-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stability of Time-Delay Systems

Author : Keqin Gu
Publisher : Springer Science & Business Media
ISBN 13 : 1461200393
Total Pages : 367 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stability of Time-Delay Systems by : Keqin Gu

Download or read book Stability of Time-Delay Systems written by Keqin Gu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained presentation of the background and progress of the study of time-delay systems, a subject with broad applications to a number of areas.

Delay Differential Equations

Author : Yang Kuang
Publisher : Academic Press
ISBN 13 : 0080960022
Total Pages : 413 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Delay Differential Equations by : Yang Kuang

Download or read book Delay Differential Equations written by Yang Kuang and published by Academic Press. This book was released on 1993-03-05 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The First 60 Years Of Nonlinear Analysis Of Jean Mawhin

Author : Manuel Delgado
Publisher : World Scientific
ISBN 13 : 9814483176
Total Pages : 266 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis The First 60 Years Of Nonlinear Analysis Of Jean Mawhin by : Manuel Delgado

Download or read book The First 60 Years Of Nonlinear Analysis Of Jean Mawhin written by Manuel Delgado and published by World Scientific. This book was released on 2004-06-29 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work of Jean Mawhin covers different aspects of the theory of differential equations and nonlinear analysis. On the occasion of his sixtieth birthday, a group of mathematicians gathered in Sevilla, Spain, in April 2003 to honor his mathematical achievements as well as his unique personality.This book provides an extraordinary view of a number of ground-breaking ideas and methods in nonlinear analysis and differential equations.List of Contributors: H Amann, M Delgado, J L Gámez, A M Krasnoselskij, E Liz, J Mawhin, P Quittner, B P Rynne, L Sanchez, K Schmitt, J R Ward, F Zanolin, and others.

Delay Differential Equations

Author : Balakumar Balachandran
Publisher : Springer Science & Business Media
ISBN 13 : 0387855955
Total Pages : 349 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Delay Differential Equations by : Balakumar Balachandran

Download or read book Delay Differential Equations written by Balakumar Balachandran and published by Springer Science & Business Media. This book was released on 2009-04-05 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delay Differential Equations: Recent Advances and New Directions cohesively presents contributions from leading experts on the theory and applications of functional and delay differential equations (DDEs). Students and researchers will benefit from a unique focus on theory, symbolic, and numerical methods, which illustrate how the concepts described can be applied to practical systems ranging from automotive engines to remote control over the Internet. Comprehensive coverage of recent advances, analytical contributions, computational techniques, and illustrative examples of the application of current results drawn from biology, physics, mechanics, and control theory. Students, engineers and researchers from various scientific fields will find Delay Differential Equations: Recent Advances and New Directions a valuable reference.

Theory of Functional Differential Equations

Author : Jack K. Hale
Publisher : Springer Science & Business Media
ISBN 13 : 146129892X
Total Pages : 374 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Theory of Functional Differential Equations by : Jack K. Hale

Download or read book Theory of Functional Differential Equations written by Jack K. Hale and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred. As a consequence, it was decided not to make a few corrections and additions for a second edition of those notes, but to present a more compre hensive theory. The present work attempts to consolidate those elements of the theory which have stabilized and also to include recent directions of research. The following chapters were not discussed in my original notes. Chapter 1 is an elementary presentation of linear differential difference equations with constant coefficients of retarded and neutral type. Chapter 4 develops the recent theory of dissipative systems. Chapter 9 is a new chapter on perturbed systems. Chapter 11 is a new presentation incorporating recent results on the existence of periodic solutions of autonomous equations. Chapter 12 is devoted entirely to neutral equations. Chapter 13 gives an introduction to the global and generic theory. There is also an appendix on the location of the zeros of characteristic polynomials. The remainder of the material has been completely revised and updated with the most significant changes occurring in Chapter 3 on the properties of solutions, Chapter 5 on stability, and Chapter lOon behavior near a periodic orbit.

Stability, Control, and Computation for Time-Delay Systems

Author : Wim Michiels
Publisher : SIAM
ISBN 13 : 1611973627
Total Pages : 443 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Stability, Control, and Computation for Time-Delay Systems by : Wim Michiels

Download or read book Stability, Control, and Computation for Time-Delay Systems written by Wim Michiels and published by SIAM. This book was released on 2014-12-11 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time delays are important components of many systems in, for instance, engineering, physics, economics, and the life sciences, because the transfer of material, energy, and information is usually not instantaneous. Time delays may appear as computation and communication lags, they model transport phenomena and heredity, and they arise as feedback delays in control loops. This monograph addresses the problem of stability analysis, stabilization, and robust fixed-order control of dynamical systems subject to delays, including both retarded- and neutral-type systems. Within the eigenvalue-based framework, an overall solution is given to the stability analysis, stabilization, and robust control design problem, using both analytical methods and numerical algorithms and applicable to a broad class of linear time-delay systems.? In this revised edition, the authors make the leap from stabilization to the design of robust and optimal controllers and from retarded-type to neutral-type delay systems, thus enlarging the scope of the book within control; include new, state-of-the-art material on numerical methods and algorithms to broaden the book?s focus and to reach additional research communities, in particular numerical linear algebra and numerical optimization; and increase the number and range of applications to better illustrate the effectiveness and generality of their approach.?

Nonlinear Dynamics

Author : Marc R Roussel
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1643274643
Total Pages : 190 pages
Book Rating : 4.6/5 (432 download)

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Book Synopsis Nonlinear Dynamics by : Marc R Roussel

Download or read book Nonlinear Dynamics written by Marc R Roussel and published by Morgan & Claypool Publishers. This book was released on 2019-05-01 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab (or its free cousin, Octave) and the Maple symbolic algebra system. Detailed instructions for various common procedures, including bifurcation analysis using the version of AUTO embedded in Xppaut, are provided. This book also provides a survey that can be taught in a single academic term covering a greater variety of dynamical systems (discrete versus continuous time, finite versus infinite-dimensional, dissipative versus conservative) than is normally seen in introductory texts. Numerical computation and linear stability analysis are used as unifying themes throughout the book. Despite the emphasis on computer calculations, theory is not neglected, and fundamental concepts from the field of nonlinear dynamics such as solution maps and invariant manifolds are presented.

Oscillation Theory of Delay Differential Equations

Author : I. Győri
Publisher : Clarendon Press
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Oscillation Theory of Delay Differential Equations by : I. Győri

Download or read book Oscillation Theory of Delay Differential Equations written by I. Győri and published by Clarendon Press. This book was released on 1991 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Solving Ordinary Differential Equations II

Author : Ernst Hairer
Publisher : Springer Science & Business Media
ISBN 13 : 3662099470
Total Pages : 615 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Solving Ordinary Differential Equations II by : Ernst Hairer

Download or read book Solving Ordinary Differential Equations II written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Whatever regrets may be, we have done our best." (Sir Ernest Shackleton, turning back on 9 January 1909 at 88°23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential alge braic equations. It contains three chapters: Chapter IV on one-step (Runge Kutta) methods for stiff problems, Chapter Von multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretieal nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered consecutively in each section and indicate, in addition, the section num ber. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.