Below-threshold Bistability and Implementation Lag in a Simplex Model of Radical Vote-Share Dynamics

[2608.27742] Below-threshold Bistability and Implementation Lag in a Simplex Model of Radical Vote-Share Dynamics Skip to main content Search Submit Donate Log in Mathematics > Dynamical Systems arXiv:2608.27742 (math) [Submitted on 27 Aug 2026] Title: Below-threshold Bistability and Implementation Lag in a Simplex Model of Radical Vote-Share Dynamics Authors: Alexander Omelchenko View PDF HTML (experimental) Abstract: We study a nonautonomous compartmental model on the probability simplex for radical vote-share dynamics under delayed policy implementation. The model distinguishes a target regime from an effective regime that adjusts with finite speed and includes a persistent alienation reservoir that can later be mobilised by radical actors. In a symmetric benchmark, persistent alienation destroys the global one-threshold picture: below the local instability threshold, a radical-free centrist--alienated equilibrium may coexist with a stable positive equilibrium, separated by a saddle branch created in a saddle-node bifurcation. By hyperbolic persistence, this coexistence survives near the symmetric baseline, while numerical exploration identifies a wider bistable region under asymmetric perturbations. Delayed implementation further separates target and effective threshold passage, producing a parameter-space lag and an additional state-space lag before a visible response in radical support. The analysis combines a Perron--Frobenius threshold for the frozen radical-free equilibrium, a geometric characterisation of positive equilibria, local adiabatic tracking under slow uniformly subcritical drift, and explicit delay bounds for transversal threshold passage. Under initial matching, the parameter-space delay scales as \(O(\kappa_\theta^{-1})\); in a monotone ramp example the bound is nearly attained, whereas the state-space lag is substantially larger and less sensitive to implementation speed. Thus threshold restoration is preventive rather than curative: once the trajectory enters the basin of the radicalised attractor, returning below the local threshold need not restore the radical-free regime. Comments: 44 pages, 8 figures. Published in Communications in Nonlinear Science and Numerical Simulation, Volume 162, Part 3, November 2026, 110392 Subjects: Dynamical Systems (math.DS) MSC classes: 34C23, 34D20, 37C60, 91F10 Cite as: arXiv:2608.27742 [math.DS] (or arXiv:2608.27742v1 [math.DS] for this version) https://doi.org/10.48550/arXiv.2608.27742 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Communications in Nonlinear Science and Numerical Simulation 162 (2026), 110392 Related DOI : https://doi.org/10.1016/j.cnsns.2026.110392 Focus to learn more DOI(s) linking to related resources Submission history From: Alexander Omelchenko [ view email ] [v1] Thu, 27 Aug 2026 22:07:49 UTC (139 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.DS < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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