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We study an influence network of voters subjected to correlated disorderedexternal perturbations, and solve the dynamical equations exactly for fullyconnected networks. The model has a critical phase transition betweendisordered unimodal and ordered bimodal distribution states, characterized byan increase in the vote-share variability of the equilibrium distributions. Therandom heterogeneities in the external perturbations are shown to affect thecritical behavior of the network relative to networks without disorder. Thesize of the shift in the critical behavior essentially depends on the totalfluctuation of the external influence disorder. Furthermore, the externalperturbation disorder also has the surprising effect of amplifying the expectedsupport of an already biased opinion. We show analytically that the vote-sharevariability is directly related to the external influence fluctuations. Weextend our analysis by considering a fat-tailed multivariate lognormaldisorder, and present numerical simulations that confirm our analyticalresults. Simulations for other network topologies demonstrate thegeneralizability of our findings. Understanding the dynamic response of complexsystems to disordered external perturbations could account for a wide varietyof networked systems, from social networks and financial markets to amorphousmagnetic spins and population genetics.

Opinion Dynamics on Networks under Correlated Disordered External Perturbations