Since the 1970s, Complex and chaotic nonlinear dynamics (in short, Complex
Dynamics) constitute a growing and increasingly important area that comprises
advanced research activities and strongly interdisciplinary approaches. This area
is of a fundamental interest in many sciences, including Economics.
Let us start with a comment about the interest of Complex Dynamics in Economics
and in so doing the necessity of such a book and its interdisciplinarity:
Mathematics in Economics have a very strong didactic role. Mathematics state theoretical
models and paradigms that must conform to measurements. However, in
Economics the measurements are rare, more often of a small number of points and
of a very low density, except for stock markets. This chasm that separates Economics
from the “dense” measurable reality has maintained economists in a kind
of “isolation” (compared with other sciences): (1) that of the qualitative approach
that can be conducted, for instance, in a literary way, very often of great relevance
but which is not quantitative, (2) and that of the construction of models (“mathematical
idealities”) with a strong didactic or mechanistic vocation often far from
the richness of “the living”. This is above all a problem of measurement. Beyond the
epistemological revolution of nonlinear theory, today there is that of the information
systems and networks, which will provide the exceptional opportunity to capture
dense measurements in numerous fields of Economics (e.g. from consumer behaviors
up to national accounts). Thus, the economists will be in an opposite situation
than before. The measure flows for the economists will have densities increasingly
similar to those of other sciences whose measures come from “the living” for example.
Economics will have to treat these measure flows with relevant tools, which are
necessary to master. This is a turning point for Economics. Thus, Mathematics and
its analytic tools are more relevant than ever for economists, in particular to study
Complex Dynamics and to bring closer theoretical models and information coming
from signal or time series measurements. Calculation capabilities, networks,
measurements and information treatment also make the existence of such a book
legitimate and necessary