E-raamat: Boundaries of a Complex World

The centraltheme of this book is the extent to which the structure of the free dynamicalboundaries of a system controls the evolution of the system as a whole. Applyingthree orthogonal types of thinking - mathematical, constructivist andmorphological, it illustrates these concepts using applications to selectedproblems from the social and life sciences, as well as economics.In a broadercontext, it introduces and reviews some modern mathematical approaches to thescience of complex systems. Standard modeling approaches (based on non-lineardifferential equations, dynamic systems, graph theory, cellular automata,stochastic processes, or information theory) are suitable for studying localproblems. However they cannot simultaneously take into account all the differentfacets and phenomena of a complex system, and new approaches are required to solvethe challenging problem of correlations between phenomena at different levelsand hierarchies, their self-organization and memo

ry-evolutive aspects, the growthof additional structures and are ultimately required to explain why and howsuch complex systems can display both robustness and flexibility. This graduate-leveltext also addresses a broader interdisciplinary audience, keeping themathematical level essentially uniform throughout the book, and involving onlybasic elements from calculus, algebra, geometry and systems theory.

Part I Arts and Nonlinear Systems: `Nonlineart".- Part II Mathematical Language.- Part III Applications.- Conclusions.- References.