theme of this book is the extent to which the structure of the free dynamical
boundaries of a system controls the evolution of the system as a whole. Applying
three orthogonal types of thinking - mathematical, constructivist and
morphological, it illustrates these concepts using applications to selected
problems from the social and life sciences, as well as economics.
In a broader
context, it introduces and reviews some modern mathematical approaches to the
science of complex systems. Standard modeling approaches (based on non-linear
differential equations, dynamic systems, graph theory, cellular automata,
stochastic processes, or information theory) are suitable for studying local
problems. However they cannot simultaneously take into account all the different
facets and phenomena of a complex system, and new approaches are required to solve
the challenging problem of correlations between phenomena at different levels
and hierarchies, their self-organization and memory-evolutive aspects, the growth
of additional structures and are ultimately required to explain why and how
such complex systems can display both robustness and flexibility.
text also addresses a broader interdisciplinary audience, keeping the
mathematical level essentially uniform throughout the book, and involving only
basic elements from calculus, algebra, geometry and systems theory.