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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.
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.
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.
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.
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