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Constructing a critical phase in a population of interacting two-state stochastic units

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  • Svenkeson, Adam
  • West, Bruce J.

Abstract

We discuss how to generate an extended critical phase by controlling, with two control parameters, the transition rates of two-state stochastic units. The Langevin equation describing the mean field dynamics becomes strongly nonlinear and admits large fluctuations everywhere in the critical phase. Appropriate construction of transition rates allows the interacting system to be tuned to a critical line with the first control parameter, and then finely tuned along the critical line with respect to a tricritical point by adjusting the second control parameter. We introduce a basic model for interacting units, a perturbation of an existing opinion dynamics model, that displays these properties of extended criticality.

Suggested Citation

  • Svenkeson, Adam & West, Bruce J., 2018. "Constructing a critical phase in a population of interacting two-state stochastic units," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 40-45.
    • Handle: RePEc:eee:chsofr:v:113:y:2018:i:c:p:40-45
    DOI: 10.1016/j.chaos.2018.05.003
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