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We study a system composed from two interdependent networks A and B, where afraction of the nodes in network A depends on the nodes of network B and afraction of the nodes in network B depends on the nodes of network A. Due tothe coupling between the networks when nodes in one network fail they causedependent nodes in the other network to also fail. This invokes an iterativecascade of failures in both networks. When a critical fraction of nodes failthe iterative process results in a percolation phase transition that completelyfragments both networks. We show both analytically and numerically thatreducing the coupling between the networks leads to a change from a first orderpercolation phase transition to a second order percolation transition at acritical point. The scaling of the percolation order parameter near thecritical point is characterized by the critical exponent beta=1.

Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition