Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.26224

Input-to-Output Stability and Consensus Control of Opinion Dynamics on Graph State-Space

Arthur Doliveira·Christophe Roman·Guillaume Graton·Mustapha Ouladsine
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper proposes a modeling of opinion dynamics in social systems with evolving structures on the Graph State-Space. It builds upon the Hegselmann-Krause (HK) model with variable influence weights, integrated into a hybrid dynamical systems framework where structural changes (agent addition/removal) are induced by inputs. We establish an Inputto-Output Stability (IOS) result under a strong connectivity assumption, using a nonsmooth Lyapunov function based on the opinion diameter; we show that the consensus expansion is then bounded by the maximal deviation of incoming agents relative to the existing convex hull. Assuming constant influence weights, we propose a consensus control result via agent injection in the social system. The results of this paper initiate, to the best of our knowledge, the analysis of resilience, stability, and control of dynamic systems on Graph State-Space.

Explore related subjects

math.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Arthur Doliveira, Christophe Roman, Guillaume Graton, Mustapha Ouladsine. 2026-10-19. Input-to-Output Stability and Consensus Control of Opinion Dynamics on Graph State-Space. https://arxiv.org/abs/2610.26224

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A coupling normal form for reversible center-center Hamiltonians with application to the restricted three-body problem

Near a reversible center-center equilibrium, the Birkhoff normal form does not describe the families bifurcating from the continued tori, which resonant normal forms capture through a reduced system.With a reflection symmetry, we develop a coupling normal form in which the bifurcating families also appear as tori of action normal forms. Along a selected coupling direction, the first harmonic in the angle difference is absorbed into an action-dependent counterterm. We prove that the coupled recursion determines unique counterterm coefficients, a formal action normal form, and an exact counterterm factorization. The factorization gives a recovery constraint, whose trivial factor corresponds to the Birkhoff normal form. At every finite order, a symmetric pair of bifurcating branches leaves the trivial branch at a critical curve, carrying approximately invariant tori and circles with residual estimates. In the spatial circular restricted three-body problem, these give approximate halo orbits and quasi-halo tori.

math.DS↗
arXiv2026

Multiplicity of closed geodesics on odd-dimensional bumpy Finsler compact space form

Let $M = S^{2n+1}/Γ$ be a manifold diffeomorphic to a compact space form, endowed with a bumpy Finsler metric $F$. In this paper, we prove that there exist at least $n+3$ contractible minimal closed geodesics on $M$, assuming that all contractible minimal closed geodesics have non-zero Morse indices. Here, a contractible closed geodesic is called minimal if it is not an iteration of any other contractible closed geodesic. In particular, this confirms the generalized Anosov-Katok conjecture for the bumpy quotient manifold $(S^3/Γ, F)$ under the non-zero Morse index assumption.

math.DS↗
arXiv2026

Ergodicity of the geodesic flow on surfaces of nonpositive curvature

We give a full proof that the geodesic flow of a closed surface of genus at least two with a \(C^{3+\mathrm{Lip}}\) metric of nonpositive curvature is ergodic with respect to Liouville measure. In a forthcoming paper, we will present the corresponding result for smooth rank-one manifolds in every dimension.

math.DS↗