Consensus and Clustering of Expressed and Private Opinions in Dynamical Networks Against Attacks

A continuous-time opinion dynamics with both expressed and private opinions on a given topic is introduced. An opinion consensus strategy is proposed to achieve resilience consensus against Byzantine attacks in dynamical networks. Necessary and sufficient criteria are established for guaranteeing consensus among normal nodes when the attacks are bounded in each neighborhood of normal nodes. A modification that allows opinion clustering, featuring nonglobal consensus, is presented. Numerical examples are worked out to illustrate the effectiveness of our theoretical results.