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Delay Differential Equations

Delay Differential Equations PDF

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Author: Yang Kuang
Publisher: Academic Press
ISBN: 9780080960029
Size: 43.71 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 398
View: 1483

Book Description: 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.


An Introduction To Delay Differential Equations With Applications To The Life Sciences

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

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Author: hal smith
Publisher: Springer Science & Business Media
ISBN: 9781441976468
Size: 55.17 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 172
View: 7090

Book Description: 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.


Applied Delay Differential Equations

Applied Delay Differential Equations PDF

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Author: Thomas Erneux
Publisher: Springer Science & Business Media
ISBN: 0387743723
Size: 22.48 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 204
View: 6592

Book Description: 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.


Oscillation Theory Of Delay Differential Equations

Oscillation Theory of Delay Differential Equations PDF

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Author: I. Győri
Publisher: Clarendon Press
ISBN:
Size: 16.81 MB
Format: PDF
Category : Delay differential equations
Languages : en
Pages : 368
View: 1468

Book Description: This monograph presents a self-contained account of the advances in the oscillation theory of this class of equations. The main topics of study are motivated by a range of diverse applications.


Stability Of Linear Delay Differential Equations

Stability of Linear Delay Differential Equations PDF

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Author: Dimitri Breda
Publisher: Springer
ISBN: 149392107X
Size: 45.21 MB
Format: PDF, Kindle
Category : Science
Languages : en
Pages : 158
View: 4208

Book Description: 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

Stability and Oscillations in Delay Differential Equations of Population Dynamics PDF

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Author: K. Gopalsamy
Publisher: Springer Science & Business Media
ISBN: 9401579202
Size: 15.61 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 502
View: 665

Book Description: 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.


Delay Differential Equations

Delay Differential Equations PDF

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Author: Balakumar Balachandran
Publisher: Springer Science & Business Media
ISBN: 0387855955
Size: 38.43 MB
Format: PDF, ePub, Mobi
Category : Technology & Engineering
Languages : en
Pages : 350
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Book Description: 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.


Ordinary And Delay Differential Equations

Ordinary and Delay Differential Equations PDF

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Author: R. D. Driver
Publisher: Springer Science & Business Media
ISBN: 1468494678
Size: 21.89 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 505
View: 615

Book Description: 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 Differential Equations And Applications

Delay Differential Equations and Applications PDF

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Author: O. Arino
Publisher: Springer Science & Business Media
ISBN: 1402036477
Size: 78.14 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 570
View: 5924

Book Description: This Edition includes detailed discussion and analysis on: General Results and Linear Theory of Delay Equations in Finite Dimensional Spaces; Hopf Bifurcation, Centre Manifolds and Normal Forms for Delay Differential Equations; Functional Differential Equations in Infinite Dimensional Spaces; and Delay Differential Equations and Applications.


Delay Differential Equations And Dynamical Systems

Delay Differential Equations and Dynamical Systems PDF

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Author: Stavros Busenberg
Publisher: Springer
ISBN: 3540474188
Size: 51.51 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 256
View: 6967

Book Description: The meeting explored current directions of research in delay differential equations and related dynamical systems and celebrated the contributions of Kenneth Cooke to this field on the occasion of his 65th birthday. The volume contains three survey papers reviewing three areas of current research and seventeen research contributions. The research articles deal with qualitative properties of solutions of delay differential equations and with bifurcation problems for such equations and other dynamical systems. A companion volume in the biomathematics series (LN in Biomathematics, Vol. 22) contains contributions on recent trends in population and mathematical biology.


Numerical Methods For Delay Differential Equations

Numerical Methods for Delay Differential Equations PDF

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Author: Alfredo Bellen
Publisher: Oxford University Press
ISBN: 0199671370
Size: 15.96 MB
Format: PDF, Docs
Category : Business & Economics
Languages : en
Pages : 410
View: 6328

Book Description: 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.