Delayed Dynamical Systems: Networks, Chimeras and Reservoir Computing

TL;DR

This paper explores the connection between delayed dynamical systems and networks of coupled oscillators, demonstrating how FPGA-based architectures can extend network complexity and control synchronization patterns for applications like reservoir computing.

Contribution

It introduces FPGA-based implementations to realize complex delayed networks with arbitrary topologies, enhancing the exploration of synchronization and dynamics in such systems.

Findings

Extended capabilities for network design using FPGAs

Controlled synchronization patterns in complex networks

Application potential in reservoir computing

Abstract

We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics, extensive research on optoelectronic feedback loops has revealed their immense potential for realizing complex system dynamics such as chimeras in rings of coupled oscillators and applications to reservoir computing. Delayed dynamical systems have been enriched in recent years through the application of digital signal processing techniques. Very recently, we have showed that one can significantly extend the capabilities and implement networks with arbitrary topologies through the use of field programmable gate arrays (FPGAs). This architecture allows the design of appropriate filters and multiple time delays which greatly extend the possibilities for exploring synchronization patterns in arbitrary topological networks. This has enabled us to explore complex dynamics on networks with nodes that can be perfectly identical, introduce parameter heterogeneities and multiple time delays, as well as change network topologies to control the formation and evolution of patterns of synchrony.