Recent Advances In Delay Differential And Difference Equations

Author : Ferenc Hartung,Mihály Pituk
Publisher : Springer
Page : 263 pages
File Size : 50,5 Mb
Release : 2014-08-22
Category : Mathematics
ISBN : 9783319082516

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Recent Advances in Delay Differential and Difference Equations by Ferenc Hartung,Mihály Pituk Pdf

Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering and control theory. In this volume, the participants of the International Conference on Delay Differential and Difference Equations and Applications, Balatonfüred, Hungary, July 15-19, 2013 present recent research in this quickly-evolving field. The papers relate to the existence, asymptotic and oscillatory properties of the solutions; stability theory; numerical approximations; and applications to real world phenomena using deterministic and stochastic discrete and continuous dynamical systems.

Author : Balakumar Balachandran,Tamás Kalmár-Nagy,David E. Gilsinn
Publisher : Springer Science & Business Media
Page : 349 pages
File Size : 47,9 Mb
Release : 2009-04-05
Category : Technology & Engineering
ISBN : 9780387855950

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Delay Differential Equations by Balakumar Balachandran,Tamás Kalmár-Nagy,David E. Gilsinn Pdf

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.

Author : K. Gopalsamy
Publisher : Springer Science & Business Media
Page : 514 pages
File Size : 45,7 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.

Author : Kai Liu,Ilpo Laine,Lianzhong Yang
Publisher : Walter de Gruyter GmbH & Co KG
Page : 276 pages
File Size : 44,5 Mb
Release : 2021-06-08
Category : Mathematics
ISBN : 9783110560404

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Complex Delay-Differential Equations by Kai Liu,Ilpo Laine,Lianzhong Yang Pdf

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Author : I. Győri,G. E. Ladas
Publisher : Clarendon Press
Page : 392 pages
File Size : 54,5 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.

Author : Thomas Erneux
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 48,7 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.

Author : SuiSun Cheng
Publisher : Routledge
Page : 206 pages
File Size : 42,5 Mb
Release : 2017-09-29
Category : Mathematics
ISBN : 9781351428804

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New Developments in Difference Equations and Applications by SuiSun Cheng Pdf

The late Professor Ming-Po Chen was instrumental in making the Third International Conference on Difference Equations a great success. Dedicated to his memory, these proceedings feature papers presented by many of the most prominent mathematicians in the field. It is a comprehensive collection of the latest developments in topics including stability theory, combinatorics, asymptotics, partial difference equations, as well as applications to biological, social, and natural sciences. This volume is an indispensable reference for academic and applied mathematicians, theoretical physicists, systems engineers, and computer and information scientists.

Author : Youssef N. Raffoul
Publisher : Academic Press
Page : 366 pages
File Size : 48,8 Mb
Release : 2022-04-13
Category : Mathematics
ISBN : 9780323992817

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Advanced Differential Equations by Youssef N. Raffoul Pdf

Advanced Differential Equations provides coverage of high-level topics in ordinary differential equations and dynamical systems. The book delivers difficult material in an accessible manner, utilizing easier, friendlier notations and multiple examples. Sections focus on standard topics such as existence and uniqueness for scalar and systems of differential equations, the dynamics of systems, including stability, with examples and an examination of the eigenvalues of an accompanying linear matrix, as well as coverage of existing literature. From the eigenvalues' approach, to coverage of the Lyapunov direct method, this book readily supports the study of stable and unstable manifolds and bifurcations. Additional sections cover the study of delay differential equations, extending from ordinary differential equations through the extension of Lyapunov functions to Lyapunov functionals. In this final section, the text explores fixed point theory, neutral differential equations, and neutral Volterra integro-differential equations. Includes content from a class-tested over multiple years with advanced undergraduate and graduate courses Presents difficult material in an accessible manner by utilizing easier, friendlier notations, multiple examples and thoughtful exercises of increasing difficulty Provides content that is appropriate for advanced classes up to, and including, a two-semester graduate course in exploring the theory and applications of ordinary differential equations Requires minimal background in real analysis and differential equations Offers a partial solutions manual for student study

Author : Saber N. Elaydi,I. Gyori,G. Ladas
Publisher : CRC Press
Page : 702 pages
File Size : 51,7 Mb
Release : 1998-01-29
Category : Mathematics
ISBN : 9056995219

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Advances in Difference Equations by Saber N. Elaydi,I. Gyori,G. Ladas Pdf

The recent surge in research activity in difference equations and applications has been driven by the wide applicability of discrete models to such diverse fields as biology, engineering, physics, economics, chemistry, and psychology. The 68 papers that make up this book were presented by an international group of experts at the Second International Conference on Difference Equations, held in Veszprém, Hungary, in August, 1995. Featuring contributions on such topics as orthogonal polynomials, control theory, asymptotic behavior of solutions, stability theory, special functions, numerical analysis, oscillation theory, models of vibrating string, models of chemical reactions, discrete competition systems, the Liouville-Green (WKB) method, and chaotic phenomena, this volume offers a comprehensive review of the state of the art in this exciting field.

Author : Taketomo Mitsui,Guang-Da Hu
Publisher : Springer Nature
Page : 118 pages
File Size : 55,8 Mb
Release : 2023-05-23
Category : Mathematics
ISBN : 9789811992636

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Numerical Analysis of Ordinary and Delay Differential Equations by Taketomo Mitsui,Guang-Da Hu Pdf

This book serves as a concise textbook for students in an advanced undergraduate or first-year graduate course in various disciplines such as applied mathematics, control, and engineering, who want to understand the modern standard of numerical methods of ordinary and delay differential equations. Experts in the same fields can also learn about the recent developments in numerical analysis of such differential systems. Ordinary differential equations (ODEs) provide a strong mathematical tool to express a wide variety of phenomena in science and engineering. Along with its own significance, one of the powerful directions toward which ODEs extend is to incorporate an unknown function with delayed argument. This is called delay differential equations (DDEs), which often appear in mathematical modelling of biology, demography, epidemiology, and control theory. In some cases, the solution of a differential equation can be obtained by algebraic combinations of known mathematical functions. In many practical cases, however, such a solution is quite difficult or unavailable, and numerical approximations are called for. Modern development of computers accelerates the situation and, moreover, launches more possibilities of numerical means. Henceforth, the knowledge and expertise of the numerical solution of differential equations becomes a requirement in broad areas of science and engineering. One might think that a well-organized software package such as MATLAB serves much the same solution. In a sense, this is true; but it must be kept in mind that blind employment of software packages misleads the user. The gist of numerical solution of differential equations still must be learned. The present book is intended to provide the essence of numerical solutions of ordinary differential equations as well as of delay differential equations. Particularly, the authors noted that there are still few concise textbooks of delay differential equations, and then they set about filling the gap through descriptions as transparent as possible. Major algorithms of numerical solution are clearly described in this book. The stability of solutions of ODEs and DDEs is crucial as well. The book introduces the asymptotic stability of analytical and numerical solutions and provides a practical way to analyze their stability by employing a theory of complex functions.

Author : Jiaoxun Kuang,Yuhao Cong
Publisher : Elsevier
Page : 312 pages
File Size : 50,9 Mb
Release : 2005
Category : Business & Economics
ISBN : 7030163176

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Stability of Numerical Methods for Delay Differential Equations by Jiaoxun Kuang,Yuhao Cong Pdf

Distributed by Elsevier Science on behalf of Science Press. Available internationally for the first time, this book introduces the basic concepts and theory of the stability of numerical methods for solving differential equations, with emphasis on delay differential equations and basic techniques for proving stability of numerical methods. It is a desirable reference for engineers and academic researchers and can also be used by graduate students in mathematics, physics, and engineering. Emphasis on the stability of numerical methods for solving delay differential equations, which is vital for engineers and researchers applying these mathematical models Introduces basic concepts and theory as well as basic techniques for readers to apply in practice Can be used as for graduate courses or as a reference book for researchers and engineers in related areas Written by leading mathematicians from Shanghai Normal University in China

Author : Stavros N. Busenberg
Publisher : Springer
Page : 268 pages
File Size : 49,9 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015049308904

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Delay Differential Equations and Dynamical Systems by Stavros N. Busenberg Pdf

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.

Author : R. D. Driver
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 54,5 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.

Author : Lynn Erbe
Publisher : Routledge
Page : 230 pages
File Size : 49,8 Mb
Release : 2017-10-02
Category : Mathematics
ISBN : 9781351426312

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Oscillation Theory for Functional Differential Equations by Lynn Erbe Pdf

Examines developments in the oscillatory and nonoscillatory properties of solutions for functional differential equations, presenting basic oscillation theory as well as recent results. The book shows how to extend the techniques for boundary value problems of ordinary differential equations to those of functional differential equations.

Author : Anonim
Publisher : Unknown
Page : 249 pages
File Size : 49,5 Mb
Release : 1991
Category : Electronic
ISBN : OCLC:1132021228

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Delay Differential Equations and Dynamical Systems by Anonim Pdf