Chaos suppression via adaptive feedback control of intermittency: From exactly solvable ergodic maps to interacting microbubble clusters

[2608.03754] Chaos suppression via adaptive feedback control of intermittency: From exactly solvable ergodic maps to interacting microbubble clusters Skip to main content Search Submit Donate Log in Nonlinear Sciences > Chaotic Dynamics arXiv:2608.03754 (nlin) [Submitted on 4 Aug 2026] Title: Chaos suppression via adaptive feedback control of intermittency: From exactly solvable ergodic maps to interacting microbubble clusters Authors: Mohammad Yahyavi , Sina Gholizadeh , Sohrab Behnia , Bilal Tanatar View PDF HTML (experimental) Abstract: Intermittency represents a fundamental route to chaos in nonlinear dynamical systems. In this work we introduce an adaptive control strategy in which the control parameter of an intermittent system is promoted to a dynamical variable that evolves autonomously under an auxiliary nonlinear map drawn from the same functional hierarchy as the system itself. The construction eliminates the need for orbit identification, local linearization, and trajectory-triggered perturbations, which are central ingredients of conventional feedback schemes. The theoretical framework is developed within a class of one-dimensional nonlinear ergodic maps with exactly known invariant (Sinai--Ruelle--Bowen) measures, for which we derive in closed form (i) the dynamics and invariant measure of the evolving control parameter, (ii) the invariant measure of the coupled system, and (iii) the $q$-generalized Lyapunov exponents before and after control. The generalized Lyapunov spectrum serves as an analytical order parameter for the control process: the collapse of its positive regions provides a quantitative and initial-condition-independent signature of chaos suppression, and yields the sensitivity to initial conditions in explicit form. To establish the physical relevance of the approach beyond low-dimensional maps, we apply the same construction to a cluster of three interacting ultrasound-driven microbubbles described by the Keller--Herring model, promoting the experimentally accessible acoustic driving frequency to a dynamical variable. Systematic bifurcation and Lyapunov analyses, performed over wide ranges of driving pressure, frequency, and equilibrium radii, demonstrate that intermittent chaotic radial oscillations are progressively suppressed and replaced by stable periodic motion. Comments: 29 pages, 15 figures Subjects: Chaotic Dynamics (nlin.CD) Cite as: arXiv:2608.03754 [nlin.CD] (or arXiv:2608.03754v1 [nlin.CD] for this version) https://doi.org/10.48550/arXiv.2608.03754 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. Research 8, 033205 (2026) Related DOI : https://doi.org/10.1103/sdfg-l9l1 Focus to learn more DOI(s) linking to related resources Submission history From: Mohammad Yahyavi [ view email ] [v1] Tue, 4 Aug 2026 14:43:52 UTC (10,859 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: nlin.CD < prev | next > new | recent | 2026-08 Change to browse by: nlin 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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