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This paper studies a stylized model of local interaction where agents choose from an ever increasing set of vertically ranked actions, e.g. technologies. The driving forces of the model are infrequent upward shifts (``updates), followed by a rapid process of local imitation (``diffusion). Our main focus is on the regularities displayed by the long-run distribution of diffusion waves and their implication on the performance of the system. By integrating analytical techniques and numerical simulations, we come to the following two main conclusions. (1) If dis-coordination costs are sufficiently high, the system behaves critically, in the sense customarily used in physics. (2) The performance of the system is optimal at the frontier of the critical region. Heuristically, this may be interpreted as an indication that (performance-sensitive) evolutionary forces induce the system to be placed ``at the edge of order and chaos
The shape of clouds has proven to be essential for classifying them. Our analysis of images from fair weather cumulus clouds reveals that, besides by turbulence they are driven by self-organized criticality (SOC). Our observations yield exponents tha
The concept of percolation is combined with a self-consistent treatment of the interaction between the dynamics on a lattice and the external drive. Such a treatment can provide a mechanism by which the system evolves to criticality without fine tuni
A system is in a self-organized critical state if the distribution of some measured events (avalanche sizes, for instance) obeys a power law for as many decades as it is possible to calculate or measure. The finite-size scaling of this distribution f
In this thesis we present few theoretical studies of the models of self-organized criticality. Following a brief introduction of self-organized criticality, we discuss three main problems. The first problem is about growing patterns formed in the abe
Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant r