THE BIFURCATION PHENOMENA OF BINARY-STATE OPINION FORMATION ON NETWORKS
The binary-state opinion model with the conservation law of public information is studied. The public information Inf i provided by node i is an exponential function of its degree with the tunable parameter β, which reflects the impact factor of the node i to his/her local neighbors. We realize our model on the top of complex networks with another tunable parameter α, which shows the degree heterogeneous as the form of the power-law degree distribution with the exponent γ = (1 + α)/α. We find that much more public information (β > 2) and less public information (β < -1) cannot let either of the two opinions win during the opinion formation. In the (α,β) space, the system undergoes the doubling bifurcation and then after a point becomes chaotic when the α decreases from 1 to 0. Maybe, our present work can provide some perspectives and tools to understand the conversation of opinion formation in our society.