The value of conflict in stable social networks

¹ Center for Nonlinear Science, University of North Texas - P.O. Box 311427, Denton, TX 76203-1427, USA
² Faculty of Science and Technology, Chiang Mai Rajabhat University - 202 Chang Phuak Road, Muang, Chiang Mai 50300, Thailand
³ Army Research Laboratory - 2800 Powder Mill Road, Adelphi, MD 20783, USA
⁴ Information Science Directorate, Army Research Office - Research Triangle Park, NC 27709, USA

Received: 18 July 2015
Accepted: 2 September 2015

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, as a finite-size effect, 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.