No Access Submitted: 17 February 2020 Accepted: 06 May 2020 Published Online: 01 June 2020
Chaos 30, 063107 (2020); https://doi.org/10.1063/5.0004826
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  • F. Bauzá
  • D. Soriano-Paños
  • J. Gómez-Gardeñes
  • L. M. Floría
In this article, we analyze a compartmental model aimed at mimicking the role of imitation and delation of corruption in social systems. In particular, the model relies on a compartmental dynamics in which individuals can transit between three states: honesty, corruption, and ostracism. We model the transitions from honesty to corruption and from corruption to ostracism as pairwise interactions. In particular, honest agents imitate corrupt peers while corrupt individuals pass to ostracism due to the delation of honest acquaintances. Under this framework, we explore the effects of introducing social intimidation in the delation of corrupt people. To this aim, we model the probability that an honest delates a corrupt agent as a decreasing function of the number of corrupt agents, thus mimicking the fear of honest individuals to reprisals by those corrupt ones. When this mechanism is absent or weak, the phase diagram of the model shows three equilibria [(i) full honesty, (ii) full corruption, and (iii) a mixed state] that are connected via smooth transitions. However, when social intimidation is strong, the transitions connecting these states turn explosive leading to a bistable phase in which a stable full corruption phase coexists with either mixed or full honesty stable equilibria. To shed light on the generality of these transitions, we analyze the model in different network substrates by means of Monte Carlo simulations and deterministic microscopic Markov chain equations. This latter formulation allows us to derive analytically the different bifurcation points that separate the different phases of the system.
We acknowledge financial support from the Spanish Ministerio de Economía y Competitividad through Project No. FIS2017-87519-P and from the Departamento de Industria e Innovación del Gobierno de Aragón y Fondo Social Europeo through Project No. E 36 _ 17R (FENOL group).
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