Coopetition and cooperosity over opinion dynamics

In the heterogeneous Hegselmann–Krause (HK) opinion dynamics network, the existence of edges among the agents depend on different connectivity thresholds. A new version of this model is here presented, by using the notions of coopetition and cooperosity. Such concepts are defined by combining the representation of the cooperation, competition and generosity behaviours. The proposed HK model is recast as a piecewise linear system with the state space partitioned into convex polyhedra defined by the agents influence functions. A sufficient condition for the local asymptotic stability, i.e., the consensus, is formulated as a set of linear matrix inequalities whose solution provides a continuous piecewise quadratic Lyapunov function. Numerical results show the effectiveness of the proposed approach.