2509.06080
From Control to Opinion Dynamics: Signum Consensus Protocol on Arbitrary Weighted Directed Graphs
Mingxi Li, Hanzhou Wang, Dongyu Li
correcthigh confidence
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:57 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper and the model both analyze the range V(x)=M(x)-m(x) for Filippov solutions of the signum-consensus dynamics with bounded disturbances, derive the same sharp differential inequality d/dt V ≤ P(W), construct worst-case selections that achieve equality until consensus, and conclude Strong Consensus iff P(W)<0 with the same least upper bound on consensus time. The model’s presentation uses Clarke subdifferentials and an upper Dini derivative; the paper formalizes the same idea via the set-valued Lie derivative for M and m separately. Minor notational differences (A versus Au) are reconciled by the paper’s equivalence theorem.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
A solid, technically correct contribution that cleanly resolves consensus criteria for signum consensus on directed weighted graphs with bounded disturbances. The key Polarization Index bridges dynamics and network structure and yields both necessary-and-sufficient conditions and a tight time bound. Proofs are sound and well organized; minor expository refinements would further enhance accessibility.