Opinion dynamics with stubborn agents over a cycle

In the literature pertaining to opinion dynamics, stubbornness of agents has been accounted for in the Taylor’s model. Although stubbornness may potentially slow down the convergence to consensus or agreement, it may not necessarily be an undesirable feature in the evolution of collective opinions, particularly when noise may corrupt the dynamics of each agent’s opinion. Having few stubborn agents in the group can, in fact, make a network more resilient to misinterpretation and miscommunications, which may be viewed as additive noise. In this paper, we study the effect of stubborn agents and their locations in a cycle graph, on noise rejection, using H
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performance measures. It is analytically proved that in case of two stubborn agents, placing them farthest apart will be better than placing them side by side, for noise rejection.