Pair approximation for the q-voter model with independence on complex networks

摘要

We investigate the q-voter model with stochastic noise arising from independence on complex networks.Using the pair approximation, we provide a comprehensive, mathematical description of its behavior and derivea formula for the critical point. The analytical results are validated by carrying out Monte Carlo experiments. Thepair approximation prediction exhibits substantial agreement with simulations, especially for networks with weakclustering and large average degree. Nonetheless, for the average degree close to q, some discrepancies originate.It is the first time we are aware of that the presented approach has been applied to the nonlinear voter dynamicswith noise. Up till now, the analytical results have been obtained only for a complete graph. We show that inthe limiting case the prediction of pair approximation coincides with the known solution on a fully connectednetwork.