Article,
Percolation on interacting, antagonistic networks
Journal of Statistical Mechanics: Theory and Experiment, 2013 (05): P05005+ (May 7, 2013)
DOI: 10.1088/1742-5468/2013/05/P05005
Abstract
Recently, new results on percolation of interdependent networks have shown
that the percolation transition can be first order. In this paper we show that,
when considering antagonistic interactions between interacting networks, the
percolation process might present a bistability of the equilibrium solution. To
this end, we introduce antagonistic interactions for which the functionality,
or activity, of a node in a network is incompatible with the functionality, of
the linked nodes in the other interacting networks. In particular, we study the
percolation transition in two interacting networks with purely antagonistic
interaction and different topology. For two antagonistic Poisson networks of
different average degree we found a large region in the phase diagram in which
there is a bistability of the steady state solutions of the percolation
process, i.e. we can find that either one of the two networks might percolate.
For two antagonistic scale-free networks we found that there is a region in the
phase diagram in which, despite the antagonistic interactions, both networks
are percolating. Finally we characterize the rich phase diagram of the
percolation problems on two antagonistic networks, the first one of the two
being a Poisson network and the second one being a scale-free network.
