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Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales

  • Book
  • © 2020

Overview

Authors:
  1. Murat Adıvar

    1. Broadwell College of Business and Economics, Fayetteville State University, Fayetteville, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Youssef N. Raffoul

    1. Department of Mathematics, University of Dayton, Dayton, USA

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    You can also search for this author in PubMed   Google Scholar

  • Synthesizes the theoretical aspect of functional dynamical systems and its applications to Volterra integrals and integro-dynamical systems on time scales

  • Presents detailed proofs of theorems

  • Allows use with mixed-level classes through accessible presentation

  • Invites further study and scholarship through open problems at the end of each chapter

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Introduction to Stability and Boundedness in Dynamical Systems

    • Murat Adıvar, Youssef N. Raffoul
    Pages 1-50

  3. Ordinary Dynamical Systems

    • Murat Adıvar, Youssef N. Raffoul
    Pages 51-90

  4. Functional Dynamical Systems

    • Murat Adıvar, Youssef N. Raffoul
    Pages 91-124

  5. Volterra Integro-Dynamic Equations

    • Murat Adıvar, Youssef N. Raffoul
    Pages 125-193

  6. Exotic Lyapunov Functionals for Boundedness and Stability

    • Murat Adıvar, Youssef N. Raffoul
    Pages 195-236

  7. Volterra Integral Dynamic Equations

    • Murat Adıvar, Youssef N. Raffoul
    Pages 237-263

  8. Periodic Solutions: The Natural Setup

    • Murat Adıvar, Youssef N. Raffoul
    Pages 265-352

  9. Periodicity Using Shift Periodic Operators

    • Murat Adıvar, Youssef N. Raffoul
    Pages 353-403

  10. Back Matter

    Pages 405-416
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Keywords

About this book

Motivated by recent increased activity of research on time scales, the book  provides a systematic approach to the study of the qualitative theory of boundedness, periodicity and stability of Volterra integro-dynamic equations on time scales. Researchers and graduate students who are interested in the method of Lyapunov functions/functionals, in the study of boundedness of solutions, in the stability of the zero solution, or in the existence of periodic solutions should be able to use this book as a primary reference and as a resource of latest findings. This book contains many open problems and should be of great benefit to those who are pursuing research in dynamical systems or in Volterra integro-dynamic equations on time scales with or without delays. Great efforts were made to present rigorous and detailed proofs of theorems. The book should serve as an encyclopedia on the construction of Lyapunov functionals in analyzing solutions of dynamical systems on time scales. The book is suitable for a graduate course in the format of graduate seminars or as special topics course on dynamical systems.



The book should be of interest to investigators in biology, chemistry, economics, engineering, mathematics and physics.

Reviews

“This monograph is aptly titled, as it offers a comprehensive overview of results on time scales related to periodicity, stability, and boundedness for functional dynamic equations. The strengths of the book are the sections and whole chapters dealing with periodicity; Lyapunov stability and Lyapunov functions; and functional dynamic equations, including Volterra integro-dynamic equations. … A nice feature of the book is the inclusion of open problems at the end of each chapter.” (Douglas R. Anderson, Mathematical Reviews, March, 2023)


“This book is organized in the classical mathematical style: definitions, lemmata, theorems, corollaries, proofs, examples, remarks, applications, etc. In each chapter, several examples are solved and open problems, which should be of great benefit to the researchers on the subject, are proposed. The book is well written and reads very well. It provides a useful reference in the field.” (Ioannis P. Stavroulakis, zbMATH 1464.34001, 2021)

Authors and Affiliations

  • Broadwell College of Business and Economics, Fayetteville State University, Fayetteville, USA

    Murat Adıvar

  • Department of Mathematics, University of Dayton, Dayton, USA

    Youssef N. Raffoul

Bibliographic Information

  • Book Title: Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales

  • Authors: Murat Adıvar, Youssef N. Raffoul

  • DOI: https://doi.org/10.1007/978-3-030-42117-5

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-42116-8Published: 14 May 2020

  • eBook ISBN: 978-3-030-42117-5Published: 23 April 2020

  • Edition Number: 1

  • Number of Pages: XIV, 416

  • Number of Illustrations: 2 b/w illustrations, 1 illustrations in colour

  • Topics: Dynamical Systems and Ergodic Theory, Real Functions

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