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Register a new userSelf-organized Model for Modular Complex Networks : Division and Independence
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We introduce a minimal network model which generates a modular structure in a self-organized way. To this end, we modify the Barabasi-Albert model into the one evolving under the principle of division and independence as well as growth and preferential attachment (PA). A newly added vertex chooses one of the modules composed of existing vertices, and attaches edges to vertices belonging to that module following the PA rule. When the module size reaches a proper size, the module is divided into two, and a new module is created. The karate club network studied by Zachary is a prototypical example. We find that the model can reproduce successfully the behavior of the hierarchical clustering coefficient of a vertex with degree k, C(k), in good agreement with empirical measurements of real world networks.
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A self-organized model with social percolation process is proposed to describe the propagations of information for different trading ways across a social system and the automatic formation of various groups within market traders. Based on the market structure of this model, some stylized observations of real market can be reproduced, including the slow decay of volatility correlations, and the fat tail distribution of price returns which is found to cross over to an exponential-type asymptotic decay in different dimensional systems.
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 tuning, thus offering a route to self-organized criticality (SOC) which in many cases is more natural than the weak random drive combined with boundary loss/dissipation as used in standard sand-pile formulations. We introduce a new metaphor, the e-pile model, and a formalism for electric conduction in random media to compute critical exponents for such a system. Variations of the model apply to a number of other physical problems, such as electric plasma discharges, dielectric relaxation, and the dynamics of the Earths magnetotail.
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 function with the lattice size is usually enough to assume that any cut off will disappear as the lattice size goes to infinity. This approach, however, can lead to misleading conclusions. In this work we analyze the behavior of the branching rate sigma of the events to establish whether a system is in a critical state. We apply this method to the Olami-Feder-Christensen model to obtain evidences that, in contrast to previous results, the model is critical in the conservative regime only.
Information processing networks are the result of local rewiring rules. In many instances, such rules promote links where the activity at the two end nodes is positively correlated. The conceptual problem we address is what network architecture prevails under such rules and how does the resulting network, in turn, constrain the dynamics. We focus on a simple toy model that captures the interplay between link self-reinforcement and a Self-Organised Critical dynamics in a simple way. Our main finding is that, under these conditions, a core of densely connected nodes forms spontaneously. Moreover, we show that the appearance of such clustered state can be dynamically regulated by a fatigue mechanism, eventually giving rise to non-trivial avalanche exponents.
Critical exponents of the infinitely slowly driven Zhang model of self-organized criticality are computed for $d=2,3$ with particular emphasis devoted to the various roughening exponents. Besides confirming recent estimates of some exponents, new quantities are monitored and their critical exponents computed. Among other results, it is shown that the three dimensional exponents do not coincide with the Bak, Tang, and Wiesenfeld (abelian) model and that the dynamical exponent as computed from the correlation length and from the roughness of the energy profile do not necessarily coincide as it is usually implicitly assumed. An explanation for this is provided. The possibility of comparing these results with those obtained from Renormalization Group arguments is also briefly addressed.
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