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 Integrodifferential Equations and Delay Models in Population Dynamics written by J. M. Cushing and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are, for the most part, the result of a course I taught at the University of Arizona during the Spring of 1977. Their main purpose is to inves tigate the effect that delays (of Volterra integral type) have when placed in the differential models of mathematical ecology, as far as stability of equilibria and the nature of oscillations of species densities are concerned. A secondary pur pose of the course out of which they evolved was to give students an (at least elementary) introduction to some mathematical modeling in ecology as well as to some purely mathematical subjects, such as stability theory for integrodifferentia1 systems, bifurcation theory, and some simple topics in perturbation theory. The choice of topics of course reflects my personal interests; and while these notes were not meant to exhaust the topics covered, I think they and the list of refer ences come close to covering the literature to date, as far as integrodifferentia1 models in ecology are concerned. I would like to thank the students who took the course and consequently gave me the opportunity and stimulus to organize these notes. Special thanks go to Professor Paul Fife and Dr. George Swan who also sat in the course and were quite helpful with their comments and observations. Also deserving thanks are Professor Robert O'Malley and Ms. Louise C. Fields of the Applied Mathematics Program here at the University of Arizona. Ms. Fields did an outstandingly efficient and accu rate typing of the manuscript.
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.
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 Stability and Stabilization of Time Delay Systems written by Wim Michiels and published by SIAM. This book was released on 2007-01-01 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overall solution to the (robust) stability analysis and stabilisation problem of linear time-delay systems.
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.
Download or read book Differential Equations and Applications Volume 4 written by Yeol Je Cho and published by Nova Publishers. This book was released on 2007-07-02 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to introduce new topics on the areas of difference, differential, integrodifferential and integral equations, evolution equations, control and optimisation theory, dynamic system theory, queuing theory and electromagnetism and their applications.
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.
Download or read book Numerical Methods for Delay Differential Equations written by Alfredo Bellen and published by OUP Oxford. This book was released on 2003-03-20 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the book is to introduce the readers to the numerical integration of the Cauchy problem for delay differential equations (DDEs). Peculiarities and differences that DDEs exhibit with respect to ordinary differential equations are preliminarily outlined by numerous examples illustrating some unexpected, and often surprising, behaviours of the analytical and numerical solutions. The effect of various kinds of delays on the regularity of the solution is described and some essential existence and uniqueness results are reported. The book is centered on the use of Runge-Kutta methods continuously extended by polynomial interpolation, includes a brief review of the various approaches existing in the literature, and develops an exhaustive error and well-posedness analysis for the general classes of one-step and multistep methods. The book presents a comprehensive development of continuous extensions of Runge-Kutta methods which are of interest also in the numerical treatment of more general problems such as dense output, discontinuous equations, etc. Some deeper insight into convergence and superconvergence of continuous Runge-Kutta methods is carried out for DDEs with various kinds of delays. The stepsize control mechanism is also developed on a firm mathematical basis relying on the discrete and continuous local error estimates. Classical results and a unconventional analysis of "stability with respect to forcing term" is reviewed for ordinary differential equations in view of the subsequent numerical stability analysis. Moreover, an exhaustive description of stability domains for some test DDEs is carried out and the corresponding stability requirements for the numerical methods are assessed and investigated. Alternative approaches, based on suitable formulation of DDEs as partial differential equations and subsequent semidiscretization are briefly described and compared with the classical approach. A list of available codes is provided, and illustrative examples, pseudo-codes and numerical experiments are included throughout the book.
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.
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.
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.
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 Optimal Control of the Growth of Wealth of Nations written by E.N. Chukwu and published by CRC Press. This book was released on 2003-01-23 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students and researchers in applied mathematics and applied economics can use this introductory-level graduate text. It looks at the current problems of the development of the global economy by studying the dynamics of key economic variables, such as gross national product, interest rates, employment, value of capital stock, prices (inflation) and
Download or read book Advances in Time Delay Systems written by Silviu-Iulian Niculescu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the mathematical description of a physical or biological process, it is a common practice \0 assume that the future behavior of Ihe process considered depends only on the present slate, and therefore can be described by a finite sct of ordinary diffe rential equations. This is satisfactory for a large class of practical systems. However. the existence of lime-delay elements, such as material or infonnation transport, of tcn renders such description unsatisfactory in accounting for important behaviors of many practical systems. Indeed. due largely to the current lack of effective metho dology for analysis and control design for such systems, the lime-delay elements arc often either neglected or poorly approximated, which frequently results in analysis and simulation of insufficient accuracy, which in turns leads to poor performance of the systems designed. Indeed, it has been demonstrated in the area of automatic control that a relatively small delay may lead to instability or significantly deteriora ted perfonnances for the corresponding closed-loop systems.
Download or read book Approximation Theory and Analytic Inequalities written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2021-07-21 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.
