From Flow to Map in an Experimental High-Dimensional Electro-Optic Nonlinear Delay Oscillator

Larger, Laurent; Lacourt, Pierre-Ambroise; Poinsot, S.; Hanna, Marc

doi:10.1103/physrevlett.95.043903

Cited by 38 publications

(29 citation statements)

References 27 publications

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“…[52]. Alternatively, the system can be turned into a discrete time map by pulsing the laser at a repetition rate f r = N/τ D [53]. In this case, the system can be modeled as…”

Section: Introduction To Optoelectronic Oscillators With Delayed Feedmentioning

confidence: 99%

Delayed dynamical systems: networks, chimeras and reservoir computing

Hart

Larger

Murphy

et al. 2019

Phil. Trans. R. Soc. A.

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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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“…[52]. Alternatively, the system can be turned into a discrete time map by pulsing the laser at a repetition rate f r = N/τ D [53]. In this case, the system can be modeled as…”

Section: Introduction To Optoelectronic Oscillators With Delayed Feedmentioning

confidence: 99%

Delayed dynamical systems: networks, chimeras and reservoir computing

Hart

Larger

Murphy

et al. 2019

Phil. Trans. R. Soc. A.

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“…Such a setup leads to an interpretation of the dynamics in terms of a much smoother limit from the flow to the map via a particular dynamical transition scenario that depends on the repetition rate of the pulsed laser. 8 Three particular characteristics associated with this scenario are:…”

Section: Experimental Chaotic Map Generated By Picosecond Laser Pulsementioning

confidence: 99%

Experimental chaotic map generated by picosecond laser pulse-seeded electro-optic nonlinear delay dynamics

Grapinet

Udaltsov

Jacquot

et al. 2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We describe experimental studies of the dynamical behavior of a recently proposed electro-optic discrete time nonlinear delay oscillator. With appropriate choice of the oscillator loop parameters and external forcing of the dynamics using a pulsed laser source, the system allows for the physical realization of a high dimensional mathematical nonlinear mapping. The dynamical features observed with this new class of discrete time delay oscillator differ significantly from those observed with similar continuous time nonlinear delay feedback oscillators and reveal the intrinsic discrete time nature of the dynamics. We also discuss specific applications to chaos communications using regularly clocked binary data.

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“…Among other technological modifications of the original Ikeda dynamics, novel EO architectures also led to a surprising modelling of this dynamics back to a map, however preserving the high-dimensional feature of the solutions [26]. Compared with the set-up in figure 1b, the modification leading here to a correct map modelling is related to the use of a high repetition rate (greater than gigahertz) mode-locked pulsed laser source.…”

Section: (I) Amplitude Parametersmentioning

confidence: 99%