Download or read book Oscillation and Dynamics in Delay Equations written by John R. Graef and published by American Mathematical Soc.. This book was released on 1992 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

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 2013-03-14 with total page 514 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.

Download or read book Oscillation and Dynamics in Delay Equations written by John R. Graef and published by . This book was released on 1991 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Oscillation Theory for Neutral Differential Equations with Delay written by D.D Bainov and published by CRC Press. This book was released on 1991-01-01 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Nonoscillation and Oscillation Theory for Functional Differential Equations written by Ravi P. Agarwal and published by CRC Press. This book was released on 2004-08-30 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Oscillation and Stability of Delay Models in Biology written by Ravi P. Agarwal and published by Springer. This book was released on 2014-06-07 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Oscillation Theory for Second Order Dynamic Equations written by Ravi P. Agarwal and published by CRC Press. This book was released on 2002-11-21 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Dynamics of Nonlinear Time Delay Systems written by Muthusamy Lakshmanan and published by Springer Science & Business Media. This book was released on 2011-01-04 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Download or read book Oscillation Theory for Functional Differential Equations written by Lynn Erbe and published by Routledge. This book was released on 2017-10-02 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Oscillation and Stability in Nonlinear Delay Differential Equations of Population Dynamics written by I. Kubiaczyk and published by . This book was released on 2018 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we shall study the oscillation of all positive solutions of the nonlinear delay differential equationandabout their equilibrium points. Also we study the stability of these equilibrium points and prove that every non-oscillatory positive solution tends to the equilibrium point when t tends to infinity. Where Eq (*) proposed by Mackey and Glass [12] for a “Dynamic Disease” involving respiratory disorders and Eq. (**) is one of the models proposed by Nazarenko [13] to study a control of a single population of cells.

Download or read book An Introduction to Nonlinear Chemical Dynamics written by Irving R. Epstein and published by Oxford University Press. This book was released on 1998-10-22 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming no more than an undergraduate knowledge of chemistry, the authors take the reader through the necessary mathematical and theoretical background of oscillating reactions, chaos and chemical waves to advanced topics of current research interest in chemical systems.

Download or read book Oscillation Theory for Second Order Linear Half Linear Superlinear and Sublinear Dynamic Equations written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the authors present a compact, thorough, systematic, and self-contained oscillation theory for linear, half-linear, superlinear, and sublinear second-order ordinary differential equations. An important feature of this monograph is the illustration of several results with examples of current interest. This book will stimulate further research into oscillation theory. This book is written at a graduate level, and is intended for university libraries, graduate students, and researchers working in the field of ordinary differential equations.

Download or read book Delay Differential Equations and Dynamical Systems written by Stavros Busenberg and published by Springer. This book was released on 2006-11-14 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book mathematical population dynamics written by Arino and published by CRC Press. This book was released on 1991-04-29 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outcome of the Second International Conference on Mathematical Population Dynamics. It is intended for mathematicians, statisticians, biologists, and medical researchers who are interested in recent advances in analyzing changes in populations of genes, cells, and tumors.

Download or read book Oscillations in Planar Dynamic Systems written by Ronald E. Mickens and published by World Scientific. This book was released on 1996 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise presentation of the major techniques for determining analytic approximations to the solutions of planar oscillatory dynamic systems. These systems model many important phenomena in the sciences and engineering. In addition to the usual perturbation procedures, the book gives the details of when and how to correctly apply the method of harmonic balance for both first-order and higher-order calculations. This procedure is rarely given or discussed fully in standard textbooks. The basic philosophy of the book stresses how to initiate and complete the calculation of approximate solutions. This is done by a clear presentation of necessary background materials and by the working out of many examples.