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

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 timescales. 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.

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

Résumé

"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)

Contenu
Introduction To Stability And Boundedness In Dynamical Systems.- Ordinary Dynamical Systems.- Functional Dynamical Systems.- Volterra Integro-dynamic Equations.- Exotic Lyapunov Functionals for Boundedness and Stability.- Volterra Integral Dynamic Eqations.- Periodic Solutions; The Natural Set up.- Periodicity Using Shift Periodic Operators.-