CONICET | Buscador de Institutos y Recursos Humanos

Recent studies have shown that in interdependent networks an initial failure of a fraction 1 − p of nodes in one network, exposes the system to a cascade of failures. Therefore it is important to develop efficient strategies to avoid their collapse. Here, we provide an exact theoretical approach to study the evolution of the cascade of failures on interdependent networks when a fraction α of the nodes with higher connectivity are autonomous. We found, for a pair of heterogeneous networks, two critical percolation thresholds that depend on α, separating three regimes with very different networks? final sizes that converge into a triple point in the plane p−α. Our findings suggest that the heterogeneity of the networks represented by high degree nodes are responsible for the rich phase diagrams found in this and other investigations.