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The Zaklan model had been proposed and studied recently using the equilibrium Ising model on Square Lattices (SL) by Zaklan et al (2008), near the critica temperature of the Ising model presenting a well-defined phase transition; but on normal and modified Apollonian networks (ANs), Andrade et al. (2005, 2009) studied the equilibrium Ising model. They showed the equilibrium Ising model not to present on ANs a phase transition of the type for the 2D Ising model. Here, using agent-based Monte-Carlo simulations, we study the Zaklan model with the well-known majority-vote model (MVM) with noise and apply it to tax evasion on ANs, to show that differently from the Ising model the MVM on ANs presents a well defined phase transition. To control the tax evasion in the economics model proposed by Zaklan et al, MVM is applied in the neighborhood of the critical noise $q_{c}$ to the Zaklan model. Here we show that the Zaklan model is robust because this can be studied besides using equilibrium dynamics of Ising model also through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.
We investigate the Majority-Vote Model with two states ($-1,+1$) and a noise $q$ on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter $q$. We also studies de effect of redirec
Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on Stauffer-Hohnisch-Pittnauer (SHP) networks. To control the fluctuations for tax evasion in the economics
We study a nonequilibrium model with up-down symmetry and a noise parameter $q$ known as majority-vote model of M.J. Oliveira $1992$ on opinion-dependent network or Stauffer-Hohnisch-Pittnauer networks. By Monte Carlo simulations and finite-size scal
Based on a theoretical model for opinion spreading on a network, through avalanches, the effect of external field is now considered, by using methods from non-equilibrium statistical mechanics. The original part contains the implementation that the a
We study a simple reaction-diffusion population model [proposed by A. Windus and H. J. Jensen, J. Phys. A: Math. Theor. 40, 2287 (2007)] on scale-free networks. In the case of fully random diffusion, the network topology cannot affect the critical de