ﻻ يوجد ملخص باللغة العربية
Cascading failures in complex systems have been studied extensively using two different models: $k$-core percolation and interdependent networks. We combine the two models into a general model, solve it analytically and validate our theoretical results through extensive simulations. We also study the complete phase diagram of the percolation transition as we tune the average local $k$-core threshold and the coupling between networks. We find that the phase diagram of the combined processes is very rich and includes novel features that do not appear in the models studying each of the processes separately. For example, the phase diagram consists of first and second-order transition regions separated by two tricritical lines that merge together and enclose a novel two-stage transition region. In the two-stage transition, the size of the giant component undergoes a first-order jump at a certain occupation probability followed by a continuous second-order transition at a lower occupation probability. Furthermore, at certain fixed interdependencies, the percolation transition changes from first-order $rightarrow$ second-order $rightarrow$ two-stage $rightarrow$ first-order as the $k$-core threshold is increased. The analytic equations describing the phase boundaries of the two-stage transition region are set up and the critical exponents for each type of transition are derived analytically.
Many real-world networks are coupled together to maintain their normal functions. Here we study the robustness of multiplex networks with interdependent and interconnected links under k-core percolation, where a node fails when it connects to a thres
In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under attacks. I
Real data show that interdependent networks usually involve inter-similarity. Intersimilarity means that a pair of interdependent nodes have neighbors in both networks that are also interdependent (Parshani et al cite{PAR10B}). For example, the coupl
The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong to the ne
K-core and bootstrap percolation are widely studied models that have been used to represent and understand diverse deactivation and activation processes in natural and social systems. Since these models are considerably similar, it has been suggested