  Antal et al. [Phys. Rev. E \textbf{72}, 036121 (2005)] have studied the
balance dynamics on the social networks. In this paper, based on the model
proposed by Antal et al., we improve it and generalize the binary social
networks to the ternary social networks. When the social networks get
dynamically balanced, we obtain the distributions of each relation and the time
needed for dynamic balance. Besides, we study the self-organized criticality on
the ternary social networks based on our model. For the ternary social networks
evolving to the sensitive state, any small disturbance may result in an
avalanche. The occurrence of the avalanche satisfies the power-law form both
spatially and temporally. Numerical results verify our theoretical
expectations.
