Laser Chimeras as a paradigm for multi-stable patterns in complex systems

Chimera is a rich and fascinating class of self-organized solutions developed in high dimensional networks having non-local and symmetry breaking coupling features. Its accurate understanding is expected to bring important insight in many phenomena observed in complex spatio-temporal dynamics, from living systems, brain operation principles, and even turbulence in hydrodynamics. In this article we report on a powerful and highly controllable experiment based on optoelectronic delayed feedback applied to a wavelength tunable semiconductor laser, with which a wide variety of Chimera patterns can be accurately investigated and interpreted. We uncover a cascade of higher order Chimeras as a pattern transition from N to N - 1 clusters of chaoticity. Finally, we follow visually, as the gain increases, how Chimera is gradually destroyed on the way to apparent turbulence-like system behaviour.Comment: 7 pages, 6 figure

Complexity in electro-optic delay dynamics: modelling, design and applications

International audienceNonlinear delay dynamics have found during the last 30 years a particularly prolific exploration area in the field of photonic systems. Besides the popular external cavity laser diode set-ups, we focus in this article on another experimental realization involving electro-optic (EO) feedback loops, with delay. This approach has strongly evolved with the important technological progress made on broadband photonic and optoelectronic devices dedicated to high-speed optical telecommunications. The complex dynamical systems performed by nonlinear delayed EO feedback loop architectures were designed and explored within a huge range of operating parameters. Thanks to the availability of high-performance photonic devices, these EO delay dynamics led also to many successful, efficient and diverse applications, beyond the many fundamental questions raised from the observation of experimental behaviours. Their chaotic motion allowed for a physical layer encryption method to secure optical data, with a demonstrated capability to operate at the typical speed of modern optical telecommunications. Microwave limit cycles generated in similar EO delay oscillators showed significantly improved spectral purity thanks to the use of a very long fibre delay line. Last but not least, a novel brain inspired computational principle has been recently implemented physically in photonics for the first time, again on the basis of an EO delay dynamical system. In this latter emerging application, the computed result is obtained by a proper 'read-out' of the complex nonlinear transients emerging from a fixed point, the transient being issued by the injection of the information signal to be processed

Delayed Dynamical Systems: Networks, Chimeras and Reservoir Computing

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

Determination of phase noise spectra in optoelectronic microwave oscillators: a Langevin approach

We introduce a stochastic model for the determination of phase noise in optoelectronic oscillators. After a short overview of the main results for the phase diffusion approach in autonomous oscillators, an extension is proposed for the case of optoelectronic oscillators where the microwave is a limit-cycle originated from a bifurcation induced by nonlinearity and time-delay. This Langevin approach based on stochastic calculus is also successfully confronted with experimental measurements.Comment: 18 pages, 7 figures, 11 references. Submitted to IEEE J. of Quantum Electronics, May 200

Intake of Fermented Vegetables and Inflammatory Markers in Women: A Pilot and Feasibility Clinical Study

The aim of this pilot study was to examine the feasibility and effect of consumption of fermented vegetables on blood markers of inflammation in women. A total of 34 women were randomized into one of three groups: fermented vegetable (Group A, n=11), non-fermented vegetable (Group B, n=13), and control (Group C, n=10). Participants in the vegetable groups were provided ½ cup of vegetables/day for six weeks, while the control group was asked to maintain their regular diet. Blood samples were collected before and after the intervention for measurement of inflammatory markers. Blood pressure, body composition, dietary intake, side effects and compliance to the intervention were assessed. Thirty-one participants completed the study. The majority of the participants were white (71%). Compliance to the interventions was 79.8% in group A and 86.5% in group B. Approximately 2.9 kg and 3.2 kg of cabbage and/or pickles per person were consumed by groups A and B, respectively, over an average of 41 days. Side effects were reported by groups A and B in 21.1% and 34.1% of the time, respectively. Median age was 35 years, body mass index, 24.1 kg/m2, and blood pressure, 114/75 mmHg. At the end of the intervention, median changes and interquartile ranges of the inflammatory markers in groups A, B, and C, respectively were: C-reactive protein: -26.8 (251), -14.2 (194), and -32.0 (545) ng/mL; tumor necrosis factor-alpha: -0.21 (0.46), -0.20 (1.50), and +0.14 (3.33) ng/mL, and lipopolysaccharide binding protein: +2.15 (7.2), -2.40 (2.4), and +0.31 (6.3) ng/mL

Optoelectronic Reservoir Computing

Reservoir computing is a recently introduced, highly efficient bio-inspired approach for processing time dependent data. The basic scheme of reservoir computing consists of a non linear recurrent dynamical system coupled to a single input layer and a single output layer. Within these constraints many implementations are possible. Here we report an opto-electronic implementation of reservoir computing based on a recently proposed architecture consisting of a single non linear node and a delay line. Our implementation is sufficiently fast for real time information processing. We illustrate its performance on tasks of practical importance such as nonlinear channel equalization and speech recognition, and obtain results comparable to state of the art digital implementations.Comment: Contains main paper and two Supplementary Material

Complex photonic nonlinear delay dynamics for high performance signal and information processing

International audienceOptoelectronic delayed feedback loops can provide a wide variety of dynamical motions, thanks to their infinite dimensional phase space. When implemented with Telecom grade components, they additionally provide broadband operation, particularly suited for high speed signal and information processing. On the basis on experimental illustration, we will introduce the fundamental nonlinear dynamical properties of photonic delayed feedback systems, from their stable fixed point operation to their high dimensional complex chaotic oscillations, through periodic oscillations. Each of these particular solution will then be further developed to demonstrate advanced information and signal processing capabilities, from secure optical chaos communications at 10Gb/s, to ultra-fast million word per second recognition through neuromorphic computing, through microwave high spectral purity oscillations for radar applications