Cooperative opinion dynamics on multiple interdependent topics: Modeling and analysis

Abstract

To model the interdependent couplings of multiple topics, we develop a set of rules for opinion updates of a group of agents. The rules are used to design or assign values to the elements of interdependent weighting matrices. The cooperative and anti-cooperative couplings are modeled in both the inverse-proportional and proportional feedbacks. The behaviors of cooperative opinion dynamics are analyzed using a null space property of state-dependent matrix-weighted Laplacian matrices and a Lyapunov candidate. Various consensus properties of state-dependent matrix-weighted Laplacian matrices are predicted according to the intra-agent network topology and inter-dependency topical coupling topologies.

Figures (10)

• Figure 1: Connected vs. Coupled: Topics $p$ and $q$, and $q$ and $r$ are coupled in the coupling graph $\mathcal{G}_{i,j}$; so the agents $i$ and $j$ are connected. But, although the agents $i$ and $j$ are connected, for example, the topics $p$ and $r$ are not coupled.
• Figure 2: Partial opinion consensus and clusters. The topic $3$ reaches a consensus, while topics $1$ and $2$ do not reach a consensus.
• Figure 3: Interaction topology of a network and coupling between neighboring topics.
• Figure 4: A network composed of four agents with three topics.
• Figure 5: Underlying topology for numerical simulations.

Theorems & Definitions (11)

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