Oscillation and Dynamics in Delay Equations
Oscillation and Dynamics in Delay Equations

Author: John R. Graef

Publisher: American Mathematical Soc.

Published: 1992

Total Pages: 274

ISBN-13: 0821851403

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Oscillation theory and dynamical systems have long been rich and active areas of research. Containing frontier contributions by some of the leaders in the field, this book brings together papers based on presentations at the AMS meeting in San Francisco in January 1991. With special emphasis on delay equations, the papers cover a broad range of topics in ordinary, partial, and difference equations and include applications to problems in commodity prices, biological modelling, and number theory. The book would be of interest to graduate students and researchers in mathematics or those in other fields who have an interest in delay equations and their applications.

Stability and Oscillations in Delay Differential Equations of Population Dynamics
Stability and Oscillations in Delay Differential Equations of Population Dynamics

Author: K. Gopalsamy

Publisher: Springer Science & Business Media

Published: 1992-03-31

Total Pages: 526

ISBN-13: 9780792315940

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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 and Oscillations in Delay Differential Equations of Population Dynamics
Stability and Oscillations in Delay Differential Equations of Population Dynamics

Author: K. Gopalsamy

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 514

ISBN-13: 9401579202

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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.

Oscillation Theory for Neutral Differential Equations with Delay
Oscillation Theory for Neutral Differential Equations with Delay

Author: D.D Bainov

Publisher: CRC Press

Published: 1991-01-01

Total Pages: 296

ISBN-13: 9780750301428

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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.

Nonoscillation and Oscillation Theory for Functional Differential Equations
Nonoscillation and Oscillation Theory for Functional Differential Equations

Author: Ravi P. Agarwal

Publisher: CRC Press

Published: 2004-08-30

Total Pages: 400

ISBN-13: 0203025741

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This book summarizes the qualitative theory of differential equations with or without delays, collecting recent oscillation studies important to applications and further developments in mathematics, physics, engineering, and biology. The authors address oscillatory and nonoscillatory properties of first-order delay and neutral delay differential eq

Oscillation and Stability of Delay Models in Biology
Oscillation and Stability of Delay Models in Biology

Author: Ravi P. Agarwal

Publisher: Springer

Published: 2014-06-07

Total Pages: 347

ISBN-13: 3319065572

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Environmental variation plays an important role in many biological and ecological dynamical systems. This monograph focuses on the study of oscillation and the stability of delay models occurring in biology. The book presents recent research results on the qualitative behavior of mathematical models under different physical and environmental conditions, covering dynamics including the distribution and consumption of food. Researchers in the fields of mathematical modeling, mathematical biology, and population dynamics will be particularly interested in this material.

Oscillation Theory for Second Order Dynamic Equations
Oscillation Theory for Second Order Dynamic Equations

Author: Ravi P. Agarwal

Publisher: CRC Press

Published: 2002-11-21

Total Pages: 416

ISBN-13: 020322289X

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The qualitative theory of dynamic equations is a rapidly developing area of research. In the last 50 years, the Oscillation Theory of ordinary, functional, neutral, partial and impulsive differential equations, and their discrete versions, has inspired many scholars. Hundreds of research papers have been published in every major mathematical journa

Dynamics of Nonlinear Time-Delay Systems
Dynamics of Nonlinear Time-Delay Systems

Author: Muthusamy Lakshmanan

Publisher: Springer Science & Business Media

Published: 2011-01-04

Total Pages: 322

ISBN-13: 3642149383

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Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different branches of science and technology as well as to the synchronization of their coupled versions. Last but not least, the presentation as a whole strives for a balance between the necessary mathematical description of the basics and the detailed presentation of real-world applications.

Oscillation Theory of Delay Differential Equations
Oscillation Theory of Delay Differential Equations

Author: I. Győri

Publisher: Clarendon Press

Published: 1991

Total Pages: 392

ISBN-13:

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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.