Coevolution of opinion dynamics on evolving signed appraisal networks (Q2071983)

This paper studies co-evolution of opinion dynamics on evolving signed appraisal networks. In a network of \(N\) agents, each agent is associated with a value \(x_i(t)\) representing its opinion at time \(t\). A weighted signed digraph \(G(W(t))\) is used to describe the interpersonal appraisals between agents. The positive elements represent positive appraisal and the negative elements represent negative appraisal. Zero elements mean non-appraisal. The co-evolution of opinions and appraisal networks is defined as \(x(t+1)=W(t)x(t)\) for opinion evolution and \(W(t+1)=f(W(t),x(t+1))\) for appraisal evolution, where \(x(t)\) forms the vector of opinions. Assume that \(G(W(t))\) achieves a state of structural balance and strongly connected components remain constant for some associated structures at time \(\tau\). Let \(H_s\) be a sink of the condensation digraph with \(N_s\) nodes at time \(t\ge\tau\). It is shown that the corresponding appraisal subnetwork converges to a fully connected structurally balanced state and the opinions of agents in it achieve a state of bipartite consensus exponentially fast. Convergence of structurally unbalanced sinks and convergence of structurally unbalanced non-sinks are also considered. Some numerical examples are presented to illustrate the results.