Delayed Dynamical Systems: Networks, Chimeras and 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.

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Cited by in corpus (18)

• Large-Scale Optical Reservoir Computing for Spatiotemporal Chaotic Systems Prediction
• Deep Neural Networks using a Single Neuron: Folded-in-Time Architecture using Feedback-Modulated Delay Loops
• Reservoir Computing and Photoelectrochemical Sensors: A Marriage of Convenience
• First-order synchronization transition in a large population of strongly coupled relaxation oscillators
• Critical Switching in Globally Attractive Chimeras
• Reservoir Computing with Noise
• Time Shifts to Reduce the Size of Reservoir Computers
• Machine Learning Link Inference of Noisy Delay-coupled Networks with Opto-Electronic Experimental Tests
• Identification of Chimera using Machine Learning
• Limit Cycles and Chaos Induced by a Nonlinearity with Memory
• Creating New Chaotic Signals with Reservoir Computers
• Laminar chaos in systems with quasiperiodic delay
• Pseudo-laminar chaos from on-off intermittency
• Dimensions of Timescales in Neuromorphic Computing Systems
• Time-shift selection for reservoir computing using a rank-revealing QR algorithm
• Emulating complex networks with a single delay differential equation
• Interpretable disorder-promoted synchronization and coherence in coupled laser networks
• Chimera states for directed networks