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Trust and distrust are common in the opinion interactions among agents insocial networks, and they are described by the edges with positive and negativeweights in the signed digraph, respectively. It has been shown in socialpsychology that although the opinions of most agents (followers) tend toprevail, sometimes one agent (leader) with a firm stand and strong influencecan impact or even overthrow the preferences of followers. This paper aims toanalyze how the leader influences the formation of followers' opinions insigned social networks. In addition, this paper considers an asynchronousevolution mechanism of trust/distrust level based on opinion difference, inwhich the trust/distrust level between neighboring agents is portrayed as anonlinear weight function of their opinion difference, and each agent interactswith the neighbors to update the trust/distrust level and opinion at the timesdetermined by its own will. Based on the related properties of sub-stochasticand super-stochastic matrices, the inequality conditions about positive andnegative weights to achieve opinion consensus and polarization are established.Some numerical simulations based on two well-known networks called the ``12Angry Men" network and the Karate Club network are provided to verify thecorrectness of the theoretical results.

Leader-Driven Opinion Dynamics in Signed Social Networks With Asynchronous Trust/Distrust Level Evolution