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.

We live in a globalized and competitive world where cities face serious mobility problems so it is important to intelligently control vehicular traffic. This article proposes the optimal cycle time that the interface (Traffic Light) must be programmed at the time of having a vehicular load on both axes (x-y) in a system of a single vehicular crossing. Based on the Monte Carlo method as a numerical technique to calculate probabilities on the average times and speeds for each combination performed in the simulator. We used a computer tool based on a programmable environment oriented to models of multi-agent systems, called NetLogo as part of the development of the research, finally describing the overall optimal behavior of the system represented graphically and mathematically.