Above the upper boundary the global cascade appears

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Unformatted text preview: nd upper ical points, for n 1,000 and z 1.05 (open squares) and z 6.14 (solid les), respectively. The straight line on the double logarithmic scale indies that cascades at the lower critical point are power-law distributed, with pe 3 2 (the cumulative distribution has slope 1 2). By contrast, the distriion at the upper critical point is bimodal, with an exponential tail at small cade size, and a second peak at the size of the entire system corresponding a single global cascade. Above the upper boundary, the global cascade appears and large cascades are always exponentially unlikely. lnerable cluster should always be sufficient to activate the entire nnected component, even when the former is a very small ction of the latter, is not an obvious result, but it appears to hold nsistently, at least within the class of random graphs. Whether or t it turns out to hold for networks more general than random phs is a matter of current investigation. Asupper 1 and 2 suggest, the onset of global cascades can occur d Figs. 14 (solid two distinct regimes—a low connectivity regime and a high ale indinn...
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