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Dynamic Systems on Measure Chains (Paperback, Softcover reprint of hardcover 1st ed. 1996)
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Dynamic Systems on Measure Chains (Paperback, Softcover reprint of hardcover 1st ed. 1996)
Series: Mathematics and Its Applications, 370
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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.GBP/LISTGBP Audience: The readership of this book consists of
applied mathematicians, engineering scientists, research workers in
dynamic systems, chaotic theory and neural nets.
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