From a modelling point of view, it is more realistic to model a
phenomenon by a dynamic system which incorporates both continuous and
discrete times, namely, time as an arbitrary closed set of reals called
time-scale or measure chain. It is therefore natural to ask whether it
is possible to provide a framework which permits us to handle both
dynamic systems simultaneously so that one can get some insight and a
better understanding of the subtle differences of these two different
systems. The answer is affirmative, and recently developed theory of
dynamic systems on time scales offers the desired unified approach.
In this monograph, we present the current state of development of the
theory of dynamic systems on time scales from a qualitative point of
view. It consists of four chapters. Chapter one develops systematically
the necessary calculus of functions on time scales. In chapter two, we
introduce dynamic systems on time scales and prove the basic properties
of solutions of such dynamic systems. The theory of Lyapunov stability
is discussed in chapter three in an appropriate setup. Chapter four is
devoted to describing several different areas of investigations of
dynamic systems on time scales which will provide an exciting prospect
and impetus for further advances in this important area which is very
new.
Some important features of the monograph are as follows:
It is the first book that is dedicated to a systematic development of
the theory of dynamic systems on time scales which is of recent origin.
It demonstrates the interplay of the two different theories, namely, the
theory of continuous and discrete dynamic systems, when imbedded in one
unified framework.
It provides an impetus to investigate in the setup of time scales other
important problems which might offer a better understanding of the
intricacies of a unified study.£/LIST£
Audience: The readership of this book consists of applied
mathematicians, engineering scientists, research workers in dynamic
systems, chaotic theory and neural nets.
