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General consensus with circular opinion under attractive and repulsive mechanisms

In this work, we study a nonlocal opinion dynamics in a ring of agents with circular opinion in the presence of both attractive and repulsive interactions. We identified three types of consensus in this model, including global consensus, local consensus, and chimera consensus. In global consensus, both local agreement among adjacent agents and global agreement among all agents are achieved. In local consensus, local agreement is satisfied but global agreement fails. There are two domains in chimera consensus, one preserves local agreement and the other breaks the local agreement. The relation between the opinion difference between adjacent agents and the interaction radius is investigated and a scaling law is found. The transitions between local consensus and chimera consensus are exemplified.