Qualitative Studies of Scalars and Systems of Difference Equations PDF Download
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Author: Elsayed M. Elsayed
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659300844
Category :
Languages : en
Pages : 208
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Book Description
The authors interested in studying the qualitative behavior (such as: local stability - global stability - periodic nature - boundedness - semi cycles analysis - oscillation - how to find the analytical forms of the solutions, etc... ) for some nonlinear difference equations and systems of difference equations as well as provide and structure mathematical models in various fields of life.
Author: Elsayed M. Elsayed
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659300844
Category :
Languages : en
Pages : 208
Get Book Here
Book Description
The authors interested in studying the qualitative behavior (such as: local stability - global stability - periodic nature - boundedness - semi cycles analysis - oscillation - how to find the analytical forms of the solutions, etc... ) for some nonlinear difference equations and systems of difference equations as well as provide and structure mathematical models in various fields of life.
Author: James Hetao Liu
Publisher:
ISBN:
Category : Differential equations, Nonlinear
Languages : en
Pages : 584
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Book Description
This book provides a complete analysis of those subjects that are of fundamental importance to the qualitative theory of differential equations and related to current research-including details that other books in the field tend to overlook. Chapters 1-7 cover the basic qualitative properties concerning existence and uniqueness, structures of solutions, phase portraits, stability, bifurcation and chaos. Chapters 8-12 cover stability, dynamical systems, and bounded and periodic solutions. A good reference book for teachers, researchers, and other professionals.
Author: Michael E. Taylor
Publisher: Springer Science & Business Media
ISBN: 1441970525
Category : Mathematics
Languages : en
Pages : 634
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Book Description
This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centred about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.
Author: Fred Brauer
Publisher: Courier Corporation
ISBN: 9780486658469
Category : Mathematics
Languages : en
Pages : 340
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Book Description
"This is a very good book ... with many well-chosen examples and illustrations." — American Mathematical Monthly This highly regarded text presents a self-contained introduction to some important aspects of modern qualitative theory for ordinary differential equations. It is accessible to any student of physical sciences, mathematics or engineering who has a good knowledge of calculus and of the elements of linear algebra. In addition, algebraic results are stated as needed; the less familiar ones are proved either in the text or in appendixes. The topics covered in the first three chapters are the standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. The next three chapters, the heart of the book, deal with stability theory and some applications, such as oscillation phenomena, self-excited oscillations and the regulator problem of Lurie. One of the special features of this work is its abundance of exercises-routine computations, completions of mathematical arguments, extensions of theorems and applications to physical problems. Moreover, they are found in the body of the text where they naturally occur, offering students substantial aid in understanding the ideas and concepts discussed. The level is intended for students ranging from juniors to first-year graduate students in mathematics, physics or engineering; however, the book is also ideal for a one-semester undergraduate course in ordinary differential equations, or for engineers in need of a course in state space methods.
Author: Youssef N. Raffoul
Publisher: Springer
ISBN: 3319971905
Category : Mathematics
Languages : en
Pages : 324
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Book Description
This book provides a comprehensive and systematic approach to the study of the qualitative theory of boundedness, periodicity, and stability of Volterra difference equations. The book bridges together the theoretical aspects of Volterra difference equations with its applications to population dynamics. Applications to real-world problems and open-ended problems are included throughout. This book will be of use as a primary reference to researchers and graduate students who are interested in the study of boundedness of solutions, the stability of the zero solution, or in the existence of periodic solutions using Lyapunov functionals and the notion of fixed point theory.
Author: Youssef N. Raffoul
Publisher: Academic Press
ISBN: 0323992811
Category : Mathematics
Languages : en
Pages : 366
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Book Description
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: Stavros Busenberg
Publisher: Springer
ISBN: 3540474188
Category : Mathematics
Languages : en
Pages : 259
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Book Description
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: Saber Elaydi
Publisher: Springer Science & Business Media
ISBN: 0387230599
Category : Mathematics
Languages : en
Pages : 547
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Book Description
A must-read for mathematicians, scientists and engineers who want to understand difference equations and discrete dynamics Contains the most complete and comprehenive analysis of the stability of one-dimensional maps or first order difference equations. Has an extensive number of applications in a variety of fields from neural network to host-parasitoid systems. Includes chapters on continued fractions, orthogonal polynomials and asymptotics. Lucid and transparent writing style
Author: Saber Elaydi
Publisher: Springer
ISBN: 3030200167
Category : Mathematics
Languages : en
Pages : 382
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Book Description
The book presents the proceedings of the 23rd International Conference on Difference Equations and Applications, ICDEA 2017, held at the West University of Timișoara, Romania, under the auspices of the International Society of Difference Equations (ISDE), July 24 - 28, 2017. It includes new and significant contributions in the field of difference equations, discrete dynamical systems and their applications in various sciences. Disseminating recent studies and related results and promoting advances, the book appeals to PhD students, researchers, educators and practitioners in the field.
Author: Saber N. Elaydi
Publisher: Springer Science & Business Media
ISBN: 1475791682
Category : Mathematics
Languages : en
Pages : 398
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Book Description
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.
