Published/Posted: May 24, 2019

Authors: Hart, J. D.; Larger, L.; Murphy, T. E.; Roy, R.

DOI: 10.1098/rsta.2018.0123

arXiv: 1808.04596

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. This architecture allows the design of appropriate filters and multiple time delays, and greatly extends the possibilities for exploring synchronization patterns in arbitrary network topologies. 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.

J. D. Hart, L. Larger, T. E. Murphy and R. Roy, "Delayed dynamical systems: networks, chimeras and reservoir computing", Phil. Trans. R. Soc. A 377(2153) 20180123 (2019)
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Manuscript: Hart_PTRSA_377_20180123_2019.pdf

Delayed dynamical systems: networks, chimeras and reservoir computing