Luis Ocampo-Espindola Jorge, Singhal Bharat, Li Jr-Shin, Kiss István Z
Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA.
Department of Electrical & Systems Engineering, Washington University in St Louis, St Louis, Missouri 63130, USA.
Chaos. 2024 Jul 1;34(7). doi: 10.1063/5.0205480.
We investigate the entrainment of electrochemical oscillators with different phase response curves (PRCs) using a global signal: the goal is to achieve the desired phase configuration using a minimum-power waveform. Establishing the desired phase relationships in a highly nonlinear networked system exhibiting significant heterogeneities, such as different conditions or parameters for the oscillators, presents a considerable challenge because different units respond differently to the common global entraining signal. In this work, we apply an optimal phase-selective entrainment technique in both a kinetic model and experiments involving electrochemical oscillators in achieving phase synchronized states. We estimate the PRCs of the oscillators at different circuit potentials and external resistance, and entrain pairs and small sets of four oscillators in various phase configurations. We show that for small PRC variations, phase assignment can be achieved using an averaged PRC in the control design. However, when the PRCs are sufficiently different, individual PRCs are needed to entrain the system with the expected phase relationships. The results show that oscillator assemblies with heterogeneous PRCs can be effectively entrained to desired phase configurations in practical settings. These findings open new avenues to applications in biological and engineered oscillator systems where synchronization patterns are essential for system performance.
我们使用一个全局信号来研究具有不同相位响应曲线（PRC）的电化学振荡器的同步：目标是使用最小功率波形实现所需的相位配置。在一个高度非线性的网络系统中建立所需的相位关系，该系统表现出显著的异质性，例如振荡器的不同条件或参数，这是一个相当大的挑战，因为不同的单元对共同的全局同步信号有不同的响应。在这项工作中，我们在动力学模型和涉及电化学振荡器的实验中应用了一种最优的相位选择同步技术，以实现相位同步状态。我们估计了振荡器在不同电路电位和外部电阻下的PRC，并使成对的和四个振荡器的小集合在各种相位配置下同步。我们表明，对于小的PRC变化，在控制设计中可以使用平均PRC来实现相位分配。然而，当PRC足够不同时，则需要使用单个PRC来使系统以预期的相位关系同步。结果表明，在实际环境中，具有异质PRC的振荡器组件可以有效地同步到所需的相位配置。这些发现为生物和工程振荡器系统的应用开辟了新途径，在这些系统中，同步模式对系统性能至关重要。
