Consensus formation simulation in a social network modeling controversial opinion dynamics with pairwise interactions

In this work, we consider a system of coupled finite-difference equations which incorporates a variety of opinion formation models, and use it to describe the dynamics of opinions on controversial subjects. The social network consists of a finite number of agents with pairwise interactions at discrete times. Meanwhile, the opinion of each agent is updated following a general nonlinear law which considers parameters identified as the personal constants of each of the members. We establish conditions that guarantee the existence of global attracting points (strong consensus) and intervals (weak consensus). Moreover, we note that these conditions are independent of the weight matrix and the number of agents of the network. Two particular scenarios are investigated numerically in order to confirm the validity of the analytical results.