  We introduce a model of percolation induced by disorder, where an initially
homogeneous network with links of equal weight is disordered by the
introduction of heterogeneous weights for the links. We consider a pair of
nodes i and j to be mutually reachable when the ratio {\alpha}_{ij} of length
of the optimal path between them before and after the introduction of disorder
does not increase beyond a tolerance ratio {\tau}. These conditions reflect
practical limitations of reachability better than the usual percolation model,
which entirely disregards path length when defining connectivity and,
therefore, communication. We find that this model leads to a first order phase
transition in both 2-dimensional lattices and in Erdos-Renyi networks, and in
the case of the latter, the size of the discontinuity implies that the
transition is effectively catastrophic, with almost all system pairs undergoing
the change from reachable to unreachable. Using the theory of optimal path
lengths under disorder, we are able to predict the percolation threshold. For
real networks subject to changes while in operation, this model should perform
better in predicting functional limits than current percolation models.
