Time-delay systems consist of delay differential equations that
combine the continuous aspect of differential equations and the
sample features of difference equations. These equations have
advanced and retarded, fixed or flexible delays. Their origin is
imputed to Condorcet in 1767, in his astronomical three-body
problem. This approach has been extensively studied in various
scientific studies in Physics, Engineering, Chemistry, Biology.
Early, the interest for such a modeling approach also appears in
Economics. In the 1930's, Kalecki presented a delay business cycle
model and Tinbergen proposed a delay system for the shipbuilding
sector. This book introduces to the main concepts and methods for
the time-delay systems with application to economics. A variety of
advanced resolution methods is presented together with numerical
examples: forward integration by steps, Lambert W function,
mathematical transforms and circuit analysis. Economic models with
delay from the standard economic theory are studied: decision
model, business cycle and growth models. The computations have been
carried out by using the softwares MATHEMATICA 7 and MATLAB 2008,
and their specialized packages.
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