AI 中文总结
以BZ反应为模型，构建弛豫振荡器温度标度的机制性解释，区分两种非阿累尼乌斯温度标度场景，发现波形不对称参数可定量预测霍普夫分岔附近多观测量的温度标度
AI 中文摘要
生物和化学振荡器的周期以特征方式随温度缩放，部分振荡器可被阿累尼乌斯（Arrhenius）定律很好描述，其余则存在系统性偏差。已有若干框架解释此类偏差，但它们要么是现象学的，要么聚焦于特定电路的活化能失衡，或仅针对 sequential 过程。本文以别洛乌索夫-扎博京斯基（Belousov-Zhabotinsky, BZ）反应为模型系统，构建弛豫振荡器温度标度的机制性解释，按温度标度特征区分两种典型场景：其一，阿累尼乌斯依赖的时间尺度分离参数使振荡器趋近霍普夫（Hopf）分岔时，周期呈现双相阿累尼乌斯标度；其二，阿累尼乌斯依赖的零倾线将同一分岔隐藏在 canard explosion 后，产生表观单线阿累尼乌斯标度。我们在约100℃的极宽温度范围内测量经典与无催化 BZ 反应的电极电势，并与动力学模型对比，发现这两种反应对应上述两种 distinct 场景。此外，我们表明表征快慢相间波形不对称性的单一参数，可定量预测霍普夫分岔附近另外三个观测量的温度标度：周期、振幅和相位噪声。该分析还得到 BZ 机制的基本活化能，包括自催化步骤的新估计值。我们讨论该框架及其基于波形的诊断方法如何应用于一般生化弛豫振荡器的分析
英文摘要
The period of biological and chemical oscillators scales with temperature in a characteristic way. Some oscillators are very well described by an Arrhenius law, while others show systematic deviations. Several frameworks have been proposed to explain such deviations, but they are either phenomenological, focus on activation energy imbalances in specific circuits, or restrict themselves to sequential processes. Here we develop a mechanistic account of the temperature scaling of relaxation oscillators, using the Belousov-Zhabotinsky (BZ) reaction as a model system. We distinguish two typical scenarios by their temperature-scaling signatures. In the first, an Arrhenius-dependent timescale separation parameter produces a biphasic Arrhenius scaling of the period as the oscillator approaches a Hopf bifurcation. In the second, Arrhenius-dependent nullclines hide the same bifurcation behind a canard explosion, yielding apparent single-line Arrhenius scaling. Measuring the electrode potential of a classical and an uncatalyzed BZ reaction, over a very wide temperature range ({\approx} 100 °C), and comparing to dynamical models, we find that the two reactions represent these two distinct scenarios. Furthermore, we show that a single parameter characterizing the waveform asymmetry between fast and slow phases quantitatively predicts the temperature scaling of three other observables close to the Hopf bifurcation: the period, amplitude, and phase noise. This analysis also recovers elementary activation energies of the BZ mechanism, including a new estimate for the autocatalytic step. We discuss how this framework and its waveform-based diagnostics apply to the analysis of general biochemical relaxation oscillators
Comments14 pages, 5 figures
