The value of conflict in stable social networks

Abstract

A cooperative network model of sociological interest is examined to determine the sensitivity of the global dynamics to having a fraction of the members behaving uncooperatively, that is, being in conflict with the majority. We study a condition where in the absence of these uncooperative individuals, the contrarians, the control parameter exceeds a critical value and the network is frozen in a state of consensus. The network dynamics change with variations in the percentage of contrarians, resulting in a balance between the value of the control parameter and the percentage of those in conflict with the majority. We show that the transmission of information from a network B to a network A, with a small fraction of lookout members in A who adopt the behavior of B, becomes maximal when both networks are assigned the same critical percentage of contrarians.

Nonergodic complexity management

“…It is important to stress that, as previously shown [41], ergodicity breaking is confined to a time region t < T eq , where T eq ∝ √ N , and N denotes the number of interacting units. We believe this to be a general property of criticality and that evaluating the transmission of information from one complex system at criticality to another complex system at criticality in the time scale t > T eq [43][44][45][46][47] gives the misleading impression that the network entrainment one finds may be a form of chaos synchronization [37]. This is a consequence of the fact that an evaluation of the correlation between the perturbed complex network and its stimulus done in the time scale t < T eq would generate the erratic behavior shown by the left panel of Fig.…”