The Heider theory of cognitive dissonance in social groups, formulatedrecently in terms of differential equations, is generalized here for the caseof asymmetric interpersonal ties. The space of initial states is penetrated bystarting the time evolution several times with random initial conditions.Numerical results show the fat-tailed distribution of the time when thedissonance is removed. For small groups (N=3) we found some characteristicpatterns of the long-living states. There, mutual relations of one of the pairsdiffer in sign.
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