Nonlinearly Coupled Amplitude Oscillators: An Experimental Study

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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.