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Discrete Oscillation Theory
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Book Synopsis Discrete Oscillation Theory by : Ravi P. Agarwal
Download or read book Discrete Oscillation Theory written by Ravi P. Agarwal and published by Hindawi Publishing Corporation. This book was released on 2005 with total page 977 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a rapidly developing branch of the qualitative theory of difference equations with or without delays. It presents the theory of oscillation of difference equations, exhibiting classical as well as very recent results in that area. While there are several books on difference equations and also on oscillation theory for ordinary differential equations, there is until now no book devoted solely to oscillation theory for difference equations. This book is filling the gap, and it can easily be used as an encyclopedia and reference tool for discrete oscillation theory. In nine chapters, the book covers a wide range of subjects, including oscillation theory for second-order linear difference equations, systems of difference equations, half-linear difference equations, nonlinear difference equations, neutral difference equations, delay difference equations, and differential equations with piecewise constant arguments. This book summarizes almost 300 recent research papers and hence covers all aspects of discrete oscillation theory that have been discussed in recent journal articles. The presented theory is illustrated with 121 examples throughout the book. Each chapter concludes with a section that is devoted to notes and bibliographical and historical remarks. The book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists. Besides serving as a reference tool for researchers in difference equations, this book can also be easily used as a textbook for undergraduate or graduate classes. It is written at a level easy to understand for college students who have had courses in calculus.
Book Synopsis Stability and Stable Oscillations in Discrete Time Systems by : Aristide Halanay
Download or read book Stability and Stable Oscillations in Discrete Time Systems written by Aristide Halanay and published by CRC Press. This book was released on 2000-10-31 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The expertise of a professional mathmatician and a theoretical engineer provides a fresh perspective of stability and stable oscillations. The current state of affairs in stability theory, absolute stability of control systems, and stable oscillations of both periodic and almost periodic discrete systems is presented, including many applications in engineering such as stability of digital filters, digitally controlled thermal processes, neurodynamics, and chemical kinetics. This book will be an invaluable reference source for those whose work is in the area of discrete dynamical systems, difference equations, and control theory or applied areas that use discrete time models.
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Book Synopsis Difference Equations, Discrete Dynamical Systems and Applications by : Martin Bohner
Download or read book Difference Equations, Discrete Dynamical Systems and Applications written by Martin Bohner and published by Springer. This book was released on 2015-12-01 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings of the 20th International Conference on Difference Equations and Applications cover the areas of difference equations, discrete dynamical systems, fractal geometry, difference equations and biomedical models, and discrete models in the natural sciences, social sciences and engineering. The conference was held at the Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences (Hubei, China), under the auspices of the International Society of Difference Equations (ISDE) in July 2014. Its purpose was to bring together renowned researchers working actively in the respective fields, to discuss the latest developments, and to promote international cooperation on the theory and applications of difference equations. This book will appeal to researchers and scientists working in the fields of difference equations, discrete dynamical systems and their applications.
Book Synopsis Difference Equations and Inequalities by : Ravi P. Agarwal
Download or read book Difference Equations and Inequalities written by Ravi P. Agarwal and published by CRC Press. This book was released on 2000-01-27 with total page 1010 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of difference equations and inequalities. This second edition offers real-world examples and uses of difference equations in probability theory, queuing and statistical problems, stochastic time series, combinatorial analysis, number theory, geometry, electrical networks, quanta in radiation, genetics, economics, psychology, sociology, and
Book Synopsis Symplectic Difference Systems: Oscillation and Spectral Theory by : Ondřej Došlý
Download or read book Symplectic Difference Systems: Oscillation and Spectral Theory written by Ondřej Došlý and published by Springer Nature. This book was released on 2019-09-06 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in this field, which are based on the recently developed central object - the comparative index. The book contains numerous results and citations, which were till now scattered only in journal papers. The book also provides new applications of the theory of matrices in this field, in particular of the Moore-Penrose pseudoinverse matrices, orthogonal projectors, and symplectic matrix factorizations. Thus it brings this topic to the attention of researchers and students in pure as well as applied mathematics.
Book Synopsis Discrete Oscillator Design by : Randall W. Rhea
Download or read book Discrete Oscillator Design written by Randall W. Rhea and published by Artech House. This book was released on 2014-05-14 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Oscillators are an essential part of all spread spectrum, RF, and wireless systems, and todayOCOs engineers in the field need to have a firm grasp on how they are designed. Presenting an easy-to-understand, unified view of the subject, this authoritative resource covers the practical design of high-frequency oscillators with lumped, distributed, dielectric and piezoelectric resonators. Including numerous examples, the book details important linear, nonlinear harmonic balance, transient and noise analysis techniques. Moreover, the book shows you how to apply these techniques to a wide range of oscillators. You gain the knowledge needed to create unique designs that elegantly match your specification needs. Over 360 illustrations and more than 330 equations support key topics throughout the book.
Book Synopsis Half-Linear Differential Equations by : Ondrej Dosly
Download or read book Half-Linear Differential Equations written by Ondrej Dosly and published by Elsevier. This book was released on 2005-07-06 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE's with p-Laplacian, half-linear difference equations and various more general nonlinear differential equations.- The first complete treatment of the qualitative theory of half-linear differential equations.- Comparison of linear and half-linear theory.- Systematic approach to half-linear oscillation and asymptotic theory.- Comprehensive bibliography and index.- Useful as a reference book in the topic.
Book Synopsis Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by : John Guckenheimer
Download or read book Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields written by John Guckenheimer and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.
Book Synopsis Jacobi Operators and Completely Integrable Nonlinear Lattices by : Gerald Teschl
Download or read book Jacobi Operators and Completely Integrable Nonlinear Lattices written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2000 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume serves as an introduction and reference source on spectral and inverse theory of Jacobi operators and applications of these theories to the Toda and Kac-van Moerbeke hierarchy.
Book Synopsis Advances in Discrete Dynamical Systems, Difference Equations and Applications by : Saber Elaydi
Download or read book Advances in Discrete Dynamical Systems, Difference Equations and Applications written by Saber Elaydi and published by Springer Nature. This book was released on 2023-03-25 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises selected papers of the 26th International Conference on Difference Equations and Applications, ICDEA 2021, held virtually at the University of Sarajevo, Bosnia and Herzegovina, in July 2021. The book includes the latest and significant research and achievements in difference equations, discrete dynamical systems, and their applications in various scientific disciplines. The book is interesting for Ph.D. students and researchers who want to keep up to date with the latest research, developments, and achievements in difference equations, discrete dynamical systems, and their applications, the real-world problems.
Book Synopsis Nonoscillation and Oscillation Theory for Functional Differential Equations by : Ravi P. Agarwal
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 392 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
Book Synopsis Ordinary Differential Equations and Dynamical Systems by : Gerald Teschl
Download or read book Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl and published by American Mathematical Society. This book was released on 2024-01-12 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
Book Synopsis Difference Equations and Discrete Dynamical Systems with Applications by : Martin Bohner
Download or read book Difference Equations and Discrete Dynamical Systems with Applications written by Martin Bohner and published by Springer. This book was released on 2021-02-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the 24th International Conference on Difference Equations and Applications, which was held at the Technical University in Dresden, Germany, in May 2018, under the auspices of the International Society of Difference Equations (ISDE). The conference brought together leading researchers working in the respective fields to discuss the latest developments, and to promote international cooperation on the theory and applications of difference equations. This book appeals to researchers and scientists working in the fields of difference equations and discrete dynamical systems and their applications.
Book Synopsis Discrete Dynamics and Difference Equations by : Saber N. Elaydi
Download or read book Discrete Dynamics and Difference Equations written by Saber N. Elaydi and published by World Scientific. This book was released on 2010 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume holds a collection of articles based on the talks presented at ICDEA 2007 in Lisbon, Portugal. The volume encompasses current topics on stability and bifurcation, chaos, mathematical biology, iteration theory, nonautonomous systems, and stochastic dynamical systems.
Book Synopsis Further Insights into Oscillation Theory by : Nikolai Verichev
Download or read book Further Insights into Oscillation Theory written by Nikolai Verichev and published by Cambridge Scholars Publishing. This book was released on 2021-07-27 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is written for students of universities and postgraduate students specializing in the field of nonlinear dynamics, as well as specialists in various fields of mechanical engineering. It is devoted to the development of original methods, and outlines the results of analytical studies of dynamical chaos, synchronization, and dynamic structures in lattices of coupled rotators. It presents its findings within the context of the phase space of models and by involving methods of the qualitative theory of differential equations, the theory of bifurcations, and qualitative numerical methods.
Book Synopsis An Introduction to Difference Equations by : Saber N. Elaydi
Download or read book An Introduction to Difference Equations written by Saber N. Elaydi and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of lecture notes I used in a course on difference equations that I taught at Trinity University for the past five years. The classes were largely pop ulated by juniors and seniors majoring in Mathematics, Engineering, Chemistry, Computer Science, and Physics. This book is intended to be used as a textbook for a course on difference equations at the level of both advanced undergraduate and beginning graduate. It may also be used as a supplement for engineering courses on discrete systems and control theory. The main prerequisites for most of the material in this book are calculus and linear algebra. However, some topics in later chapters may require some rudiments of advanced calculus. Since many of the chapters in the book are independent, the instructor has great flexibility in choosing topics for the first one-semester course. A diagram showing the interdependence of the chapters in the book appears following the preface. This book presents the current state of affairs in many areas such as stability, Z-transform, asymptoticity, oscillations and control theory. However, this book is by no means encyclopedic and does not contain many important topics, such as Numerical Analysis, Combinatorics, Special functions and orthogonal polyno mials, boundary value problems, partial difference equations, chaos theory, and fractals. The nonselection of these topics is dictated not only by the limitations imposed by the elementary nature of this book, but also by the research interest (or lack thereof) of the author.
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