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Author: Youssef N. Raffoul Publisher: Springer ISBN: 3319971905 Category : Mathematics Languages : en Pages : 333
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: Springer ISBN: 3319971905 Category : Mathematics Languages : en Pages : 333
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
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: Steve Baigent Publisher: Springer Nature ISBN: 3030601072 Category : Mathematics Languages : en Pages : 440
Book Description
This book comprises selected papers of the 25th International Conference on Difference Equations and Applications, ICDEA 2019, held at UCL, London, UK, in June 2019. The volume details the latest research on difference equations and discrete dynamical systems, and their application to areas such as biology, economics, and the social sciences. Some chapters have a tutorial style and cover the history and more recent developments for a particular topic, such as chaos, bifurcation theory, monotone dynamics, and global stability. Other chapters cover the latest personal research contributions of the author(s) in their particular area of expertise and range from the more technical articles on abstract systems to those that discuss the application of difference equations to real-world problems. The book is of interest to both Ph.D. students and researchers alike who wish to keep abreast of the latest developments in difference equations and discrete dynamical systems.
Author: James Hetao Liu Publisher: ISBN: Category : Juvenile Nonfiction Languages : en Pages : 584
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: Youssef N. Raffoul Publisher: Elsevier ISBN: 0443314934 Category : Mathematics Languages : en Pages : 340
Book Description
Difference Equations and Applications provides unique coverage of high-level topics in the application of difference equations and dynamical systems. The book begins with extensive coverage of the calculus of difference equations, including contemporary topics on l_p stability, exponential stability, and parameters that can be used to qualitatively study solutions to non-linear difference equations, including variations of parameters and equations with constant coefficients, before moving on to the Z-Transform and its various functions, scalings, and applications. It covers systems, Lyapunov functions, and stability, a subject rarely covered in competitor titles, before concluding with a comprehensive section on new variations of parameters. Exercises are provided after each section, ranging from an easy to medium level of difficulty. When finished, students are set up to conduct meaningful research in discrete dynamical systems. In summary, this book is a comprehensive resource that delves into the mathematical theory of difference equations while highlighting their practical applications in various dynamic systems. It is highly likely to be of interest to students, researchers, and professionals in fields where discrete modeling and analysis are essential. - Provides a class-tested resource used over multiple years with advanced undergraduate and graduate courses - Presents difficult material in an accessible manner by utilizing easy, friendly notations, multiple examples, and thoughtful exercises of increasing difficulty - Requires minimal background in real analysis and differential equations - Covers new and evolving topic areas, such as stability, and offers a partial solutions manual for in book exercises
Author: Ted A. Burton Publisher: Elsevier ISBN: 0080459552 Category : Mathematics Languages : en Pages : 369
Book Description
Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations. This book seeks to present Volterra integral and functional differential equations in that same framwork, allowing the readers to parlay their knowledge of ordinary differential equations into theory and application of the more general problems. Thus, the presentation starts slowly with very familiar concepts and shows how these are generalized in a natural way to problems involving a memory. Liapunov's direct method is gently introduced and applied to many particular examples in ordinary differential equations, Volterra integro-differential equations, and functional differential equations. By Chapter 7 the momentum has built until we are looking at problems on the frontier. Chapter 7 is entirely new, dealing with fundamental problems of the resolvent, Floquet theory, and total stability. Chapter 8 presents a solid foundation for the theory of functional differential equations. Many recent results on stability and periodic solutions of functional differential equations are given and unsolved problems are stated. - Smooth transition from ordinary differential equations to integral and functional differential equations - Unification of the theories, methods, and applications of ordinary and functional differential equations - Large collection of examples of Liapunov functions - Description of the history of stability theory leading up to unsolved problems - Applications of the resolvent to stability and periodic problems
Author: Saber Elaydi Publisher: Springer Nature ISBN: 303125225X Category : Mathematics Languages : en Pages : 534
Book Description
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.
Author: SuiSun Cheng Publisher: Routledge ISBN: 1351428802 Category : Mathematics Languages : en Pages : 382
Book Description
The late Professor Ming-Po Chen was instrumental in making the Third International Conference on Difference Equations a great success. Dedicated to his memory, these proceedings feature papers presented by many of the most prominent mathematicians in the field. It is a comprehensive collection of the latest developments in topics including stability theory, combinatorics, asymptotics, partial difference equations, as well as applications to biological, social, and natural sciences. This volume is an indispensable reference for academic and applied mathematicians, theoretical physicists, systems engineers, and computer and information scientists.
Author: Peter Linz Publisher: SIAM ISBN: 9781611970852 Category : Mathematics Languages : en Pages : 240
Book Description
Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods. The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises.
Author: Youssef N. Raffoul
Author: Youssef N. Raffoul
Author: Youssef N. Raffoul
Author: Steve Baigent
Author: James Hetao Liu
Author: Youssef N. Raffoul
Author: Ted A. Burton
Author: Saber Elaydi
Author: SuiSun Cheng
Author: Peter Linz
Author: B. G. Zhang