Kinetic-exchange-like opinion dynamics in complex networks: roles of the dimensionality and local interaction topology

We study a kinetic-exchange-like opinion dynamics model with both positive and negative interactions in various complex networks. The control parameter p ∈ [0, 1] denotes the probability of the presence of negative outcome in the pairwise interaction, which indicates that the difference between the standpoints of the two focal individuals becomes even more large because of disagreement. Accordingly, with probability 1 − p they become more similar (positive interaction). The average opinion of the population serves as the order parameter of the system. We find that in random homogeneous networks the ordering process displays an anomalous jump at some special value of the control parameter p*, which gives rise to two distinct critical points pc for p p*, respectively. Whenever the underlying interaction network has heterogeneous interaction patterns and/or planar property, the anomalous ordering phenomenon disappears. Finite-size scaling analysis of the simulation results shows that the critical exponents for the opinion dynamics in random networks are in accordance with those of the mean-field Ising model, no matter whether the degree distribution is homogeneous or heterogeneous and the anomalous jump of the order parameter is presence or absence. The critical exponents for the opinion dynamics in spatially embedded networks (in two dimensions) belong to different universality classes, which depend closely on the configuration of local interactions. Particularly, whenever the local interactions are homogeneously distributed, two-dimensional Ising model universality class is recovered. Mean-field theoretical analysis corroborates well our findings. Our results highlight the importance of both the dimensionality and the local topology of the underlying interaction network in the phase transition behavior of the opinion dynamics.