Journal
PHYSICAL REVIEW E
Volume 71, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.71.057104
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In many complex systems, for the activity f(i) of the constituents or nodes i a power-law relationship was discovered between the standard deviation sigma(i) and the average strength of the activity: sigma(i) (proportional to) < f(i)>(alpha); universal values alpha= 1/2 or 1 were found, however, with exceptions. With the help of an impact variable we present a random walk model where the activity is the product of the number of visitors at a node and their impact. If the impact depends strongly on the node connectivity and the properties of the carrying network are broadly distributed (as in a scale-free network) we find both analytically and numerically nonuniversal alpha values. The exponent always crosses over to the universal value of 1 if the external drive dominates.
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