Percolation on interdependent networks with a fraction of antagonistic interactions

Abstract

Recently, the percolation transition has been characterized on interacting networks both in presence of interdependent and antagonistic interactions. Here we characterize the phase diagram of the percolation transition in two Poisson interdependent networks with a percentage q of antagonistic nodes. We show that this system can present a bistability of the steady state solutions, and both first, and second order phase transitions. In particular, we observe a bistability of the solutions in some regions of the phase space also for a small fraction of antagonistic interactions 0<q<0.4. Moreover, we show that a fraction q>q_c=2/3 of antagonistic interactions is necessary to strongly reduce the region in phase-space in which both networks are percolating. This last result suggests that interdependent networks are robust to the presence of antagonistic interactions. Our approach can be extended to multiple networks, and to complex boolean rules for regulating the percolation phase transition.

(17 pages, 9 figures)

References in corpus (11)

• Synchronization in complex networks
• Critical phenomena in complex networks
• Diffusion dynamics on multiplex networks
• Network Physiology reveals relations between network topology and physiological function
• Network Synchronization, Diffusion, and the Paradox of Heterogeneity
• Avalanche Collapse of Interdependent Network
• Dynamics of jamming transitions in complex networks
• Congestion phenomena on complex networks
• Griffiths phases on complex networks
• Stability of Boolean Multilevel Networks
• Enhancement of Tc in the Superconductor-Insulator Phase Transition on Scale-Free Networks

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• Percolation on Networks with Antagonistic and Dependent Interactions
• Fragility and anomalous susceptibility of weakly interacting networks
• Resilience of antagonistic networks with regard to the effects of initial failures and degree-degree correlations