Percolation Analysis in a Fractal Network with Stable Opinion Dynamics

Abstract

This paper presents the proposal of a stable non-consensus opinion model in an infinitely branched fractal network, analyzing how its percolation properties are affected and based on the Ising model that allows the stable coexistence of three states, forming two groups of agents that hold contrary opinions and a third group that assumes a state of indecision The model is structured in a Sierpinski folder in which its fractal attributes are characterized by the dimensions of Hausdorff (DH), topological Hausdorff (DtH) and the spectral dimension (ds) since in these the values of the critical exponents of percolation are determined by the set of numbers of the dimensions (DH, DtH, ds), rather than solely by spatial dimension (d). Our findings suggest that starting from a random distribution of agents to which initial conditions are given, and employing a stable opinion dynamic through numerical simulation to calculate the percolation threshold and its critical exponents, the kind of universality to which the model belongs is determined and how the fractal characteristics in an infinitely branched network affect its percolation properties.