Interaction, Evolution and Chaos in Space

This book presents a unified framework (based on spatial interaction models) that encapsulates most of the models developed so far for the analyses of spatial patterns of human activities at both a static and a dynamic level. The book shows how such models can be associated in a static analysis, with macro- and meso-oriented entropy theory and micro-oriented random utility theory. In a dynamic analysis such models can be seen as the result of an optimal trajectory through which a closed system approaches an equilibrium state, in both a deterministic and stochastic framework. However spatial interaction models can exhibit chaotic patterns under particular conditions, since they can be linked to both a logistic form (in a degenerate case) and interrelated logistics (in a general case). Finally, such models may serve to form a broad "envelope" incorporating many dynamic models currently used, which end up with logistic structures. The theoretical-methodological foundations are original, as various tools originating from different disciplines (e.g. economics, mathematics, physics, statistics, biology and natural sciences) are used to develop a unified framework.