Exploring Coupled Oscillator Networks with Highly-Configurable Integrated Circuit Designs
Creators: name: Salwa, Yasmeen Neyaz
name: Schiek, Michael
name: Ashok, Arun
name: Grewing, Christian
name: Ebrahimzadeh, Pezhman
name: Zambanini, Andre
name: van Waasen, Stefan
Publisher: name: Forschungzentrum Jülich
Year: 2024

description: XLIV- Dynamic Days conference 2024, DDE 2024, Bremen, University of Duisburg Essen, Germany, 28 Jul 2024 - 2 Aug 2024
description: The analysis of the complex dynamics of coupled oscillator networks is crucial not only for the understanding of corresponding systems in biology (i.e., brain dynamics) but also for our technical world (e.g., the stability of power grids). Moreover, this knowledge paves the way to use coupled oscillator systems for bio-inspired computing. Both analytical methods and, in particular, numerical simulations have provided fundamental insights into the existence and coexistence of synchronization states and different symmetry breaking in completely symmetrical oscillator networks such as chimera states or solitary states [1]. For example, the influence of the coupling strength and the phase shift in the coupling on the network dynamics was investigated in detail [2]. However, despite the computing power of modern computers available today, there are limits to analyzing very large networks and their transient or adaptive dynamic over very long periods using numerical simulations. A way to overcome these restrictions is to perform experiments with physical implementations of large-scale coupled oscillator systems using state-of-the-art integrated circuit technology. Most of the recently presented developments focus on bio-inspired computing applications and thus are rather restricted concerning the configurability of network topology and coupling terms [3]. To mimic the response of real-world oscillatory networks like power grids to varying external and internal conditions, one needs to be able to change coupling topology and coupling terms of the physical implemented during the experiment, i.e., ‘on the fly’. In our proposed integrated circuit system designed in a 28 nm CMOS technology, we employ an architecture, organizing oscillators into clusters with adjustable all-to-all coupling within each cluster. A high level of configurability allows for programmable coupling terms (phase shift and coupling strength) within and between the clusters. The oscillators are realized by type 2 Phase Locked Loop (PLL) circuits of third order. The voltage-controlled oscillators (VCOs) are implemented using ring oscillators, which are well-known standard CMOS building blocks. The connectivity among the PLLs is studied with two alternative approaches, either by employing multiple phase and frequency detectors (PFD) and logic gates leading to the charge pump node or with multiple charge pumps directed towards a VCO node. The eigenfrequency of the nodes can be configured individually, typically lying in the range of 10 MHz. External inputs can be fed into dedicated nodes by either modulating the frequency or initialization of phrases of the controlled oscillators. The system dynamics are determined during operation in terms of phase and frequency synchronization within and between the clusters and this information is available in real-time, e.g., for control purposes. The proposed system is very well suited for exploring the complex long-term dynamics of large-scale oscillator networks.[1] Maistrenko, Y., Penkovsky, B., &amp; Rosenblum, M.; Physical Review E (2014).[2] Ebrahimzadeh, P., Schiek, M., &amp; Maistrenko, Y.; CHAOS (2022)[3] Csaba, G., &amp; Porod, W.; Applied physics reviews (2020)