Figure 5 Size of the Giant Component (IMAGE)

Queen Mary University of London

Figure 5 Size of the Giant Component

Caption

The size of the giant component R as a function of p for di erent values of ! is shown for the Ythan Estuary (panel (a)) and the Silwood Park (panel (b)) Foodwebs [46]. We observe that for ! > 0 the percolation transition is discontinuous while for ! = 0 we obtain the typical scenario of percolation characterized by a continuous phase transition. The non-convex rate function I(R) evaluated numerically over 2105 initial realization of the random damage is shown for the Ythan Estuary (panel (c)) and the Silwood Park (panel (d)) Foodwebs and di erent value of p (symbols). The convex envelop of I(R) provided by the Legendre-Fenchel transform of !F(!)=N is shown with solid lines for the same values of p (note that for improving the clarity of the gure we have omitted to plot the linear part of the convex envelop for p = 0:24; 0:28 in panel (c) and for p = 0:20; 0:24 in panel (d)).

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Ginestra Bianconi

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