AI 中文总结
本研究提出一种自适应反馈控制策略，可抑制一维可精确求解遍历映射及Keller-Herring模型描述的三微泡簇的间歇性混沌径向振荡，为混沌控制提供了新途径。
AI 中文摘要
间歇性是非线性动力系统通向混沌的基本途径。本研究引入一种自适应控制策略，将间歇性系统的控制参数提升为动力学变量，该变量在与系统自身功能层级相同的辅助非线性映射作用下自主演化。该构造消除了传统反馈方案中轨道识别、局部线性化及轨迹触发扰动等核心要素。理论框架在一类具有精确已知不变测度（Sinai-Ruelle-Bowen测度）的一维非线性遍历映射中构建，针对此类映射，我们以闭式形式推导得到：(i) 演化控制参数的动力学与不变测度；(ii) 耦合系统的不变测度；(iii) 控制前后的q-广义李雅普诺夫指数。广义李雅普诺夫谱作为控制过程的分析序参数：其正区域的坍缩为混沌抑制提供了与初始条件无关的定量特征，并以显式形式给出对初始条件的敏感性。为确立该方法在低维映射之外的物理相关性，我们将相同构造应用于由Keller-Herring模型描述的三个相互作用超声驱动微泡簇，将实验可测的声驱动频率提升为动力学变量。在驱动压力、频率及平衡半径的宽范围内进行的系统分岔与李雅普诺夫分析表明，间歇性混沌径向振荡被逐步抑制，替换为稳定的周期运动。
英文摘要
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.
Comments29 pages, 15 figures
Journal refPhys. Rev. Research 8, 033205 (2026)
