Organizing Principle for Tipping Points in Social Networks

摘要

In this talk ppt given at Dr Mubarak Shah's Center for Research in Vision at U Central Florida, Orlando, March 25-26 2013, we describe the overarching principles that guides the recent work on Tipping points and committed Minorities in Signalling Multi-Agent Social Networks. We find that a scalar stochastic Differential equation can be derived to give good estimates of the first exit times such as consensus times and to study the influence of diehards. For very large populations we find that a one-dimensional center manifold on which the mean-field dynamics in slow time is easily shown to consist of nodes and saddle and heteroclinic orbits linking these equilibria - the saddle node bifurcation then led to an easy determination of the critical value of diehard fraction needed to accelerate the network to consensus in the minority opinion. For smaller crowds on the order of 1000-5000 agents, we find that the demographic noise reflected in simulations by the significant variance in consensus times, must be taken into account to determine accurate estimates of the expected value of consensus times and to study the effects of committed minority.