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Chaos suppression via adaptive feedback control of intermittency

Mohammad Yahyavi1,*, Sina Gholizadeh1, Sohrab Behnia2,†, and Bilal Tanatar1,‡

  • *Contact author: mohammad.yahyavi@ntu.edu.sg
  • †Contact author: S.behnia@sci.uut.ac.ir
  • ‡Contact author: tanatar@fen.bilkent.edu.tr
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Phys. Rev. Research 8, 033205 – Published 18 August, 2026

DOI: https://doi.org/10.1103/sdfg-l9l1

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 (1) the dynamics and invariant measure of the evolving control parameter, (2) the invariant measure of the coupled system, and (3) 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. These results establish intermittency regulation as a unifying and physically realizable mechanism for stabilizing complex nonlinear dynamics.

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Phys. Rev. Research 8, 033205– Published 18 August, 2026
  • Received 1 February 2026
  • Revised 30 April 2026
  • Accepted 22 July 2026
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