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Additional info for Complexity Theory and Network Centric Warfare (Information Age Transformation Series)

Example text

These model multiperiodic and chaotic behaviour, which is observed under appropriate experimental conditions. Nonequilibrium phenomena show a variety of behaviours and therefore correspond to the movements of the system towards The Far-from-Equilibrium State Chapter 1 15 different attractors. The simplest mechanism to depict this is the bifurcation diagram, where a single control parameter (the thermal gradient in the case of Benard cells) affects the dynamics of the system. BIFURCATIONS AND UNIVERSALITY LIMITS Consider a system described by a set of evolution laws of the form of the equation: dX i = Fi ( X 1 ,...

Power-laws, in this sense lack characteristic scale. for example the standard text Chaos and Fractals by Heinz-Otto Peitgen, Hartmut Jürgens and Dietmar Sauape. Springer. 1992. 5See Clustering in Space and Time 24 Complexity Theory and Network Centric Warfare Despite this, very little (until now) has been known about why fractals form. Fractal structures are not the lowest energy configuration that can be selected in, for example, thermodynamic systems, therefore some kind of dynamic selection of configuration must be taking place.

At each step of the process, we assume that the force element with the smallest fitness is likely to have to adapt fastest to its local environment. , there is local coevolution). Note that these force elements may be separated by large and varying distances in space. With these assumptions, over time the force elements will form clusters of coevolution of the form predicted by the Bak-Sneppen model. In particular, the statistics of emergent cluster size can be predicted mathematically to converge to a power-law.

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