Nonlinearly Coupled Amplitude Oscillators: An Experimental Study

硅的电化学氧化表现为一个振荡模型系统，该系统中电极不同区域之间的耦合是非线性和非局部的，其局部动力学在一定的参数范围内表现出先天性的节律性。到目前为止观察到的典型的集体行为，如多频簇和部分振幅死亡，表现出明显的振幅动力学，其描述需要平面振荡器。这个主要实验项目的目标是有助于理解(a)非线性和非局部耦合振幅振荡器中的集体现象，以及(b)耦合生节律元件的同步和开关行为。我们将研究当非线性和非局部耦合导致有效的自适应耦合时，不同振荡域（或振子）之间的耦合强度以自组织的方式适应，什么机制负责多频簇的形成，以及自适应耦合可以诱导哪些其他集体现象。对出生节律系统的研究将集中于系统如何响应异质初始条件，其中系统的一部分（振荡器的一部分）在两个共存的极限环之一上初始化，而另一部分在另一个上初始化。对于这两个习题集，将使用两种类型的硅电极，一种具有较大的活性区域，另一种是介观上较小的活性区域被惰性基质包围。因此，前者代表一个空间连续振荡介质，后者则是一个耦合的单个振荡器网络。在每种情况下，实验都辅以模型模拟。

The electrochemical oxidation of silicon presents an oscillatory model system in which the coupling between different regions of the electrode is nonlinear and nonlocal, and whose local dynamics exhibit birhythmicity in certain parameter ranges. Typical collective behavior observed so far, such as multi-frequency clusters and partial amplitude death, exhibited distinct amplitude dynamics, the description of which requires planar oscillators. The goals of this mainly experimental project are to contribute to the understanding of (a) collective phenomena in nonlinearly and nonlocally coupled amplitude oscillators, and (b) the synchronization and switching behavior of coupled birhythmic elements. We will investigate when nonlinear and nonlocal coupling leads to effective adaptive coupling, in which the coupling strengths between different oscillating domains (or oscillators) adapt in a self-organized manner, what mechanism is responsible for the formation of the multi-frequency clusters, and what other collective phenomena can be induced by adaptive coupling. Investigations with the birhythmic systems will focus on how the system responds to heterogeneous initial conditions where part of the system (part of the oscillators) is initialized on one of the two coexisting limit cycles and the other part is initialized on the other.For both problem sets, two types of silicon electrodes will be used, ones with a large active region and ones in which mesoscopically small active regions are surrounded by an inert matrix. The former thus represent a spatially continuous oscillatory medium, the latter type a network of coupled, individual oscillators. In each case, the experiments are complemented by model simulations.