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 beta, 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 alpha, which shows the degree heterogeneous as the form of the power-law degree distribution with the exponent gamma = (1 + alpha)/alpha. We find that much more public information (beta > 2) and less public information (beta < -1) cannot let either of the two opinions win during the opinion formation. In the (alpha, beta) space, the system undergoes the doubling bifurcation and then after a point becomes chaotic when the alpha 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.