Nonequilibrium Zaklan model on Apollonian Networks

TL;DR

This paper demonstrates that the Zaklan model for tax evasion control exhibits a well-defined phase transition when using the nonequilibrium majority-vote model on Apollonian networks, showing robustness across different dynamics and topologies.

Contribution

It introduces the use of the nonequilibrium majority-vote model on Apollonian networks to study the Zaklan model, revealing a phase transition not present in the equilibrium Ising model.

Findings

MVM on ANs shows a clear phase transition.

Zaklan model's behavior is robust across dynamics and topologies.

Abstract

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.