Topology-Biased Resource Constraints Shape Synchronization Pathways in Hindmarsh-Rose Oscillator Networks

[2608.23993] Topology-Biased Resource Constraints Shape Synchronization Pathways in Hindmarsh-Rose Oscillator Networks Skip to main content Search Submit Donate Log in Nonlinear Sciences > Adaptation and Self-Organizing Systems arXiv:2608.23993 (nlin) [Submitted on 25 Aug 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Topology-Biased Resource Constraints Shape Synchronization Pathways in Hindmarsh-Rose Oscillator Networks Authors: Zhouqi Li , Xiaoyan He , Yuanhong Bi , Zengping Zhang View PDF HTML (experimental) Abstract: In oscillator networks sustained by finite resources, synchronization can depend on both the total resource and its spatial distribution. We study a duplex system whose activity layer consists of chaotic Hindmarsh--Rose oscillators and whose transport layer redistributes a conserved resource through a degree-biased Markov process. The stationary resource field is characterized analytically, and its existence, uniqueness, and convergence are established. By embedding this field into a local adaptive feedback law, the available resource is converted into node-dependent dissipation, for which Lyapunov analysis guarantees convergence to the synchronization manifold. Numerical results show that topology bias reorganizes the transient route to synchronization. Weak bias produces an almost collective contraction, whereas intermediate bias creates a hub-initiated recruitment hierarchy that extends toward middle-degree and peripheral nodes. Under stronger bias, the degree hierarchy becomes more pronounced while peripheral recruitment slows because adaptive dissipation is concentrated on structurally privileged nodes. Across the explored parameter range, this localization--coverage tradeoff is accompanied by a non-monotonic synchronization response at fixed total resource. The largest Lyapunov exponent remains positive after synchronization and the correlation dimension changes only modestly, consistent with suppression of transverse deviations while chaotic motion is retained on the synchronization manifold. Subjects: Adaptation and Self-Organizing Systems (nlin.AO) ; Chaotic Dynamics (nlin.CD) Cite as: arXiv:2608.23993 [nlin.AO] (or arXiv:2608.23993v2 [nlin.AO] for this version) https://doi.org/10.48550/arXiv.2608.23993 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Zhouqi Li [ view email ] [v1] Tue, 25 Aug 2026 02:33:58 UTC (12,335 KB) [v2] Thu, 27 Aug 2026 08:11:01 UTC (12,335 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: nlin.AO < prev | next > new | recent | 2026-08 Change to browse by: nlin nlin.CD 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. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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