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The Eckhaus instability is a secondary instability of nonlinear spatiotemporal patterns in which high-wave-number periodic solutions become unstable against small-wave-number perturbations. Here we show that this instability can take place in Kerr combs corresponding to subcritical Turing patterns upon changes in the laser detuning. The development of the Eckhaus instability leads to the cracking of patterns and a long-lived transient where the peaks of the pattern rearrange in space due to spatial interactions. In the spectral domain, this results in a metastable Kerr comb dynamics with timescales that can be larger than 1 min. This time is, at least, seven orders of magnitude larger than the intracavity photon lifetime and is in sharp contrast with all the transient behaviors reported so far in cavity nonlinear optics that are typically only a few photon lifetimes long (i.e., in the picosecond to the microsecond range). This phenomenology, studied theoretically in the Lugiato-Lefever model and the observed dynamics is compatible with experimental observations in Kerr combs generated in ultra-high-Q whispering-gallery mode resonators., D.G. and Y.K.C. acknowledge support from Project ND-PHOT jointly funded by CSIC and CNRS. D.G. and P.C. acknowledge financial support from Agencia Estatal de Investigación (AEI, Spain) and Fondo Europeo de Desarrollo Regional under Project ESoTECoS, Grant No. FIS2015-63628-C2-1-R (AEI/FEDER,UE) and Agencia Estatal de Investigación through the María de Maeztu Program for Units of Excellence in R&D (Grant No. MDM-2017-0711). Y.K.C. also acknowledges funding from the European Research Council through the Projects NextPhase and Versyt from the Centre National d'Etudes Spatiales (CNES) through Project SHYRO. PPR acknowledges funding from the H2020 Marie Skłodowska-Curie Actions through the Project NOSTER (101023717).

The ongoing energy transition challenges the stability of the electrical power system. Stable operation of the electrical power grid requires both the voltage (amplitude) and the frequency to stay within operational bounds. While much research has focused on frequency dynamics and stability, the voltage dynamics has been neglected. Here, we study frequency and voltage stability in the case of simple networks via linear stability and bulk analysis. In particular, our linear stability analysis of the network shows that the frequency secondary control guarantees the stability of a particular electric network. Even more interesting, while we only consider secondary frequency control, we observe a stabilising effect on the voltage dynamics, especially in our numerical bulk analysis., This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 840825. E.B.T.T. and P.P. acknowledge funding from the European Regional Development Fund under Grant No. CZ.02.1.02/0.0/0.0/15003/0000493, ‘CENDYNMAT – Centre of Excellence for Nonlinear Dynamics Behaviour of Advanced Materials in Engineering’ and the Academy of Sciences CR under Grant Strategy AV21, VP03: ‘Efficient energy conversion and storage, Vibrodiagnostics of rotating blades of rotary machines in power engineering. E.B.T.T. and P.C. acknowledge funding from project PACSS RTI2018-093732-B-C22 of the MCIN/AEI /10.13039/501100011033/ and by EU through FEDER funds (A way to make Europe), and also from the Maria de Maeztu program MDM-2017-0711 of the MCIN/AEI /10.13039/501100011033/. E.B.T.T. also acknowledges the fellowship from the AEI and MINEICO, Spain under the FPI program(No. FIS2015-63628-CZ-Z-R).

This work deals with the signal propagation in a model for chain of self-sustained electrical circuits with unidirectional coupling. We report on periodic and noisy inputs transmission along the chain based on theoretical and numerical investigations. The effects of additional nonlinearities and noisy fluctuations in the chain units are also highlighted in this paper. Different phenomena which appear in the chain include double amplification, chaos and fast filtering phenomenon under certain conditions. We also demonstrate that additional quartic and cubic nonlinearities have, respectively, the effect to increase or decrease the signal amplitude. The obtained results can be applicable in the design of a network of autonomous electrical generators to power micro-mechanical arms for micro-machines., This work was supported by the i-COOP program of the Spanish Consejo Superior de Investigaciones Científicas, grant number COOPB20476. D.G. and P.C. also acknowledge funding from the Ministerio de Ciencia e Innovación (Spain), the Agencia Estatal de Investigación (AEI, Spain) and the Fondo Europeo de Desarrollo Regional (FEDER, EU) under Grant No. PACSS (RTI2018-093732-B-C22) and the Maria de Maeztu program for Units of Excellence in R&D (No. MDM-2017-0711).

[ES] This data-paper presents and describes a consolidated, harmonized, internationally comparable database to quantify the impacts of the housing affordability crisis. Local harmonized indicators allow to examine the unequal spatial patterns of housing affordability across a selection of European cities. This study seeks at informing and mapping the increased and unequal affordability gap, a critical issue for social cohesion and sustainability in metropolitan areas in Europe. We characterize affordability with measures of price (property and rent) and income in a selection of European Functional Urban Areas (FUAs). The methodological goal was to cope with a data gap, i.e. a lack of harmonized spatial data to map and analyze affordability in Europe. This research, conducted in 2018-19 by a European consortium for the ESPON agency, covers 4 countries and one cross-border region: Geneva (Switzerland), Annecy-Annemasse, Avignon and Paris (France), Madrid, Barcelona and Palma de Majorca (Spain) and Warsaw, Łódź and Krakow (Poland). We bring insights on how institutional data (i.e. transactions data), can be bridged with unconventional data (“big data” harvested on line) to provide a cost-effective and harmonized data collection effort that can contribute to compare affordability within cities (between neighborhoods) and across cities, using various geographical levels (1km square-grid, municipalities, FUA). We present the structure of the database, how it has been constructed in a reproducible manner; we document the validation process, the strengths and limitations of the data provided, and document the reproducibility of the workflow., [FR] Cet article présente et décrit une base de données consolidée, harmonisée et comparable au niveau international pour quantifier les impacts de la crise de l'accessibilité (ou abordabilité) du logement. Cette base de données permet de caractériser l’inégale abordabilité du logement dans une sélection de métropoles européennes, une question cruciale pour la cohésion sociale et la durabilité dans les zones métropolitaines en Europe. La question porte sur l’inégalité d’accès au logement, en fonction des revenus. Mais cet écart s’est creusé au cours des dernières décennies : depuis les années 1990, les prix des logements ont en moyenne augmenté plus vite que les revenus des résidents et des acheteurs. La base de données caractérise l’abordabilité à l’aide de mesures du prix (propriété et loyer) et du revenu dans une sélection de zones urbaines fonctionnelles européennes (Functional Urban Areas, FUA). L’objectif méthodologique est de combler une lacune, c’est-à-dire l’absence de données spatiales harmonisées pour cartographier et analyser l’accessibilité financière en Europe. Cette étude, menée en 2018-19 par un consortium européen pour ESPON, couvre 4 pays de la zone et une région transfrontalière : Genève (Suisse), Annecy-Annemasse, Avignon et Paris (France), Madrid, Barcelone et Palma de Majorque (Espagne) et Varsovie, Łódź et Cracovie (Pologne). Nous apportons un éclairage sur la manière dont les données institutionnelles (données sur les transactions) peuvent être rapprochées des données collectées en ligne, et harmonisées pour contribuer à comparer l’accessibilité financière au sein des villes (entre les quartiers) et entre les villes, en utilisant différents niveaux géographiques (grille carroyée de 1 km, municipalités, FUA). Nous présentons la structure de la base de données, comment elle a été construite de manière reproductible ; nous documentons le processus de validation, les forces et les limites des données fournies, et documentons la reproductibilité de l’analyse., [ES] Este artículo presenta y describe una base de datos consolidada, armonizada e internacionalmente comparable para cuantificar los impactos de la crisis de acceso a la vivienda, un tema crucial para la cohesión social y sostenibilidad en las áreas metropolitanas de Europa. La base de datos caracteriza tal proceso en una muestra de las metrópolis europeas, abordando la interrogante sobre la desigualdad en el acceso a la vivienda en función de los ingresos, brecha que se ha visto incrementada en las últimas décadas. Desde los años 1990, los precios de la vivienda en promedio han aumentado más rápido que los ingresos de residentes y compradores. La base de datos caracteriza el acceso utilizando medidas de precio (propiedad y arriendo) e ingresos en una selección de áreas urbanas funcionales europeas (FUA). El objetivo metodológico es contribuir al vacío y falta de datos espaciales armonizados para cartografiar y analizar la accesibilidad financiera en Europa. Este estudio, realizado en 2018-19 por un consorcio europeo para ESPON, cubre 4 países de la zona y una región transfronteriza: Ginebra (Suiza); Annecy-Annemasse, Aviñón y París (Francia); Madrid, Barcelona y Palma de Mallorca (España); Varsovia, Lodz y Cracovia (Polonia). El trabajo aporta cómo los datos institucionales (datos en las transacciones) pueden vincularse con los datos recopilados en línea y armonizar una base para contribuir a comparar la accesibilidad financiera al interior de las ciudades (entre barrios) y entre ciudades, utilizando diferentes escalas geográficas (cuadrícula de 1 km, municipios, FUA). Presentamos y documentamos la estructura de la base de datos, su elaboración y validación, las fortalezas y limitaciones de los datos proporcionados, y la reproducibilidad del análisis., The transactions BIEN proprietary database was made available by Paris Notaire Service, on the behalf of the Chamber of the Notaries, under an agreement contracted by the LabEx DynamiTe (ANR-11-LABX-0046) consortium and the Univ. Paris 1 Pantheon-Sorbonne. Data provided by the INSEE (1 km grid) contains public sector information, made available under ©INSEE, 2013. Mattia Mazzoli is funded by the Conselleria d’Innovació, Recerca i Turisme of the Government of the Balearic Islands and the European Social Fund with grant code FPI/2090/2018. J.J.R., M.M. and P.C. also acknowledge funding from the Spanish Ministry of Science and Innovation, the AEI and FEDER (EU) under the grant PACSS (RTI2018-093732-B-C22) and the Maria de Maeztu program for Units of Excellence in R&D (MDM-2017-0711).

We propose a method to analyze the risk of blackouts with high penetration of variable renewable energy sources (VRESs). We consider a model for the long-term evolution of the power grid including propagation of cascading failures, day-to-day fluctuations of renewable generation and moderate use of storage. We analyze grid resilience and stress as VRESs are progressively incorporated. We also evaluate the VRES performance as the average fraction of daily demand covered by renewables.We find that in general, VRES intrinsic variability increases the grid stress and the blackout risk. However, if VRESs are implemented in a distributed way, the spatial spreading of the generation may have a positive effect on grid resilience. As a case study, we analyze the replacement of conventional power plants by solar photovoltaic generation combined with storage in the power grid of the Balearic Islands. We also consider the use of source redundancy and briefly discuss the potential of wind energy. The work of Pere Colet and Damià Gomila was supported in part by the Ministerio de Ciencia e Innovación, Spain, in part by the Agencia Estatal de Investigación (AEI), Spain, in part by the Fondo Europeo de Desarrollo Regional (FEDER, EU) under Grant PACSS RTI2018-093732-B-C22, and in part by the Maria de Maeztu Program for Units of Excellence in Research and Development under Grant MDM-2017-0711. The work of Benjamín A. Carreras and José M. Reynolds-Barredo was supported by the Universidad Carlos III de Madrid, Spain, funded jointly by EU FEDER funds and by the Spanish Government through the National Research Project UNC313-4E-2361, Project ENE2009-12213-C03-03, Project ENE2012-33219, and Project ENE2012-31753 (for providing access to Uranus, a supercomputer cluster).

We investigate the effects of environmental stochastic fluctuations on Kerr optical frequency combs. This spatially extended dynamical system can be accurately studied using the Lugiato-Lefever equation, and we show that when additive noise is accounted for, the correlations of the modal field fluctuations can be determined theoretically. We propose a general theory for the computation of these field fluctuations and correlations, which is successfully compared to numerical simulations., Y. K. C. acknowledges financial support the University of Maryland through the Minta Martin Fellowship

The propagation of failures and blackouts in electric networks is a complex problem. Typical models, such as the ORNL-PSerc-Alaska (OPA), are based on a combination of fast and a slow dynamics. The first describes the cascading failures while the second the grid evolution though line and generation upgrades as well as demand growth, all taking place in time scales from days to years. The growing integration of renewable energy sources, whose power fluctuates in time scales from seconds to hours, together with the increase in demand, which also present fast fluctuations, require the incorporation of distributed methods of control in the demand side to avoid the high cost of ordinary control in conventional power plants. In this work, we extend the OPA model to include fluctuations in the demand at time scales of the order of minutes, intraday demand variations and the effect of demand control. We find that demand control effectively reduces the number of blackouts without increasing the probability of large-scale events., The authors E.B.T.T., D.G. and P.C. acknowledge fund-ing from Ministerio de Ciencia e Innovación (Spain), theAgencia Estatal de Investigación (AEI, Spain), and the Fondo Europeo de Desarrollo Regional (FEDER, EU) under grant PACSS (RTI2018-093732-B-C22) and the Maria de Maeztu program for Units of Excellence in R&D (MDM-2017-0711).E.B.T.T. also acknowledges the fellowship FIS2015-63628-CZ-Z-R under the FPI program of AEI and MINEICO, Spain.B.A.C. and J.M.R.-B. acknowledge access to Uranus, a super-computer cluster located at Universidad Carlos III de Madrid(Spain).

Monitoring migration flows is crucial to respond to humanitarian crisis and to design efficient policies. This information usually comes from surveys and border controls, but timely accessibility and methodological concerns reduce its usefulness. Here, we propose a method to detect migration flows worldwide using geolocated Twitter data. We focus on the migration crisis in Venezuela and show that the calculated flows are consistent with official statistics at country level. Our method is versatile and far-reaching, as it can be used to study different features of migration as preferred routes, settlement areas, mobility through several countries, spatial integration in cities, etc. It provides finer geographical and temporal resolutions, allowing the exploration of issues not contemplated in official records. It is our hope that these new sources of information can complement official ones, helping authorities and humanitarian organizations to better assess when and where to intervene on the ground., MM is funded by the Conselleria d’Innovaci\’o, Recerca i Turisme of the Government of the Balearic Islands and the European Social Fund with grant code FPI/2090/2018. AT acknowledges financial support from the AEI, Spanish National Research Agency, with grant code PTA2017-13872-I and the Government of the Balearic Islands. MM, AT, PC and JJR also acknowledge funding from the Spanish Ministry of Science, Innovation and Universities, the AEI and FEDER (EU) under the grant PACSS (RTI2018-093732-B-C22) and the Maria de Maeztu program for Units of Excellence in R\&D (MDM-2017-0711). We acknowledge support of the publication fee by the CSIC Open Access Publication Support Initiative through its Unit of Information Resources for Research (URICI).

In a recent work, it was shown that sinusoidal signals are amplified in an array of unidirectionnally coupled MEMS and when the number of MEMS units was large enough, an instability leading to chaotic behavior was observed [M.V. Tchakui et al., Eur. Phys. J. B 89, 22 (2016)]. In this work, we explore the role of disorder in natural frequencies on the propagation and amplification of a signal in such an array. Considering a random Gaussian distribution of natural frequencies, it is found that for small disorder strength, the propagation takes place leading to oscillations in the array. Along the network, a decrease of oscillations amplitude is observed in proportion as the disorder strength grows up. With large coupling strength, the second transition to chaotic behavior is further postponed to a large MEMS rank up to its disappearance as the disorder strength increases in a broaden frequency range. For very large disorder strength the signal amplitude is damped to zero and there appears oscillationsdeath. Graphical abstract: [Figure not available: see fulltext.].

The gathering and harmonisation of international statistical data in a multidisciplinary environment are key to international comparative analysis and policy work. The availability of timely, accurate statistical information enables policy-makers, practitioners, researchers and other stakeholders to address a wide range of issues in today’s rapidly-evolving global economic and social landscape.The use of traditional data such as official administrative statistics however has some shortcomings. Traditional data in general takes long to be published and used because they are subject to a long technical and sometimes political process of harmonization and validation. Also, traditional data does not cover all topics of interest for territorial cohesion.Increasingly, data and information from analysing internet activities or social media can be used for observing territorial development trends. New developments for the availability and use of big data may help to overcome the shortcomings and bring new and interesting opportunities to support policy with up-to-date information relevant for territorial analysis.Currently, the interest from policy makers is growing as the sources for Big Data (Facebook, Google, Twitter, Instagram or blogs for example) contain valuable information, which can normally be hard to gather, and these data can be collected with very short notice. This means that Big Data could provide a more regular, cost-effective and harmonised data collection and provide an opportunity to more easily address new issues of interest.The aim of this ESPON activity is to further develop ways and methodologies for using existing big data sources and platforms to develop and measure indicators for territorial monitoring and analysis. In addition, these methodologies should be applied for indicators measuring the housing dynamics in European cities and the wellbeing of European citizens, in particular related to their housing and living situation. Finally, these methodologies should be made available and applicable to others for measuring these and other aspects in cities.

Information on ESPON and its projects can be found on www.espon.eu. The web site provides the possibility to download and examine the most recent documents produced by finalised and ongoing ESPON projects.

Understanding human mobility is crucial for applications such as forecasting epidemic spreading, planning transport infrastructure and urbanism in general. While, traditionally, mobility information has been collected via surveys, the pervasive adoption of mobile technologies has brought a wealth of (real time) data. The easy access to this information opens the door to study theoretical questions so far unexplored. In this work, we show for a series of worldwide cities that commuting daily flows can be mapped into a well behaved vector field, fulfilling the divergence theorem and which is, besides, irrotational. This property allows us to define a potential for the field that can become a major instrument to determine separate mobility basins and discern contiguous urban areas. We also show that empirical fluxes and potentials can be well reproduced and analytically characterized using the so-called gravity model, while other models based on intervening opportunities have serious difficulties., M.M. and A.B. are funded by the Conselleria d’Innovació, Recerca i Turisme of the Government of the Balearic Islands and the European Social Fund. M.M., A.B., P.C., and J.J.R. also acknowledge partial funding from the Spanish Ministry of Science, Innovation and Universities, the National Agency for Research Funding AEI and FEDER (EU) under the grants ESOTECOS (FIS2015-63628-C2-1-R and FIS2015-63628-C2-2-R) and PACSS (RTI2018-093732-B-C22) and the Maria de Maeztu program for Units of Excellence in R&D (MDM-2017-0711). M.L. received financial support from a grant of the French National Research Agency (project NetCost, ANR-17-CE03-0003).

The increase of the electric demand and the progressive integration of renewable energy sources threatens the stability of the power grid. To solve this issue, several methods have been proposed to control the demand side instead of increasing the spinning reserve in the supply. Here we focus on dynamic demand control (DDC), a method in which smart devices can autonomously delay its scheduled operation if the electric frequency is outside a suitable range. While typical control schemes can effectively reduce small and medium size frequency fluctuations, the probability of large demand peaks, and hence large frequency fluctuation, may increase due to the need of recovering pending tasks. Although these events are rare they can potentially trigger a failure of the system and therefore strategies to avoid them need to be addressed. In this work we introduce a method including communication among DDC devices belonging to a given group, such that they can coordinate opposite actions to keep the group demand more stable. We show that, with minimal information exchange, our method reduces the amount of pending tasks by a factor 10 while large frequency fluctuations are significantly reduced or even completely avoided., We acknowledge financial support from Agencia Estatal de Investigación (AEI, Spain) and Fondo Europeo de Desarrollo Regional under Project ESoTECoS, Grant Nos.: FIS2015-63628-C2-1-R (AEI/FEDER,UE) and FIS2015-63628-C2-2-R (AEI/FEDER,UE) and Agencia Estatal de Investigación through María de Maestu Program for Units of Excellence in R&D (MDM-2017-0711). E.B.T.T. also acknowledges the fellowship FIS2015-63628-CZ-Z-R under the FPI program of AEI, Spain.

Topical Issue: Theory and applications of the Lugiato-Lefever Equation., Bound states, also called soliton molecules, can form as a result of the interaction between individual solitons. This interaction is mediated through the tails of each soliton that overlap with one another. When such soliton tails have spatial oscillations, locking or pinning between two solitons can occur at fixed distances related with the wavelength of these oscillations, thus forming a bound state. In this work, we study the formation and stability of various types of bound states in the Lugiato-Lefever equation by computing their interaction potential and by analyzing the properties of the oscillatory tails. Moreover, we study the effect of higher order dispersion and noise in the pump intensity on the dynamics of bound states. In doing so, we reveal that perturbations to the Lugiato-Lefever equation that maintain reversibility, such as fourth order dispersion, lead to bound states that tend to separate from one another in time when noise is added. This separation force is determined by the shape of the envelope of the interaction potential, as well as an additional Brownian ratchet effect. In systems with broken reversibility, such as third order dispersion, this ratchet effect continues to push solitons within a bound state apart. However, the force generated by the envelope of the potential is now such that it pushes the solitons towards each other, leading to a null net drift of the solitons., We acknowledge support from the Research Foundation-Flanders (FWO-Vlaanderen) (P.P.-R.), the Belgian Science Policy Office (BelSPO) under Grant No. IAP 7-35, the Research Council of the Vrije Universiteit Brussel, and Agencia Estatal de Investigación (AEI, Spain) and Fondo Europeo de Desarrollo Region al under Project ESoTECoS FIS2015-63628-C2-1-R (AEI/FEDER,UE) (D.G. and P.C.).

Power grid frequency control is a demanding task requiring expensive idle power plants to adapt the supply to the fluctuating demand. An alternative approach is controlling the demand side in such a way that certain appliances modify their operation to adapt to the power availability. This is especially important to achieve a high penetration of renewable energy sources. A number of methods to manage the demand side have been proposed. In this work we focus on dynamic demand control (DDC), where smart appliances can delay their switchings depending on the frequency of the system. We introduce a simple model to study the effects of DDC on the frequency of the power grid. The model includes the power plant equations, a stochastic model for the demand that reproduces, adjusting a single parameter, the statistical properties of frequency fluctuations measured experimentally, and a generic DDC protocol. We find that DDC can reduce small and medium-size fluctuations but it can also increase the probability of observing large frequency peaks due to the necessity of recovering pending task. We also conclude that a deployment of DDC around 30–40% already allows a significant reduction of the fluctuations while keeping the number of pending tasks low., We acknowledge helpful discussions with B. A. Carreras and financial support from Agencia Estatal de Investigación (AEI, Spain) and Fondo Europeo de Desarrollo Regional under Project No. ESoTECoS Grants No. FIS2015-63628-C2-1-R (AEI/FEDER,UE) and No. FIS2015-63628-C2-2-R (AEI/FEDER,UE). E.B.T.-T. also acknowledges the fellowship FIS2015-63628-CZ-Z-R under the FPI program of MINEICO, Spain.

This paper investigates the resilience of an elementary electricity system (machine-generator) under proportional and derivative (PD) control when subject to large perturbations. A particular attention is paid to small power grids, representative of power grid structure in some developing countries. The considered elementary electricity system consists of a consumer (machine), a power plant (generator) and a transmission line. Both Runge-Kutta and Newton methods are used to solve the dynamical equations and the characteristic equations for stability. It is found that the controller increases the resilience of the system. We also show that time delays associated to the feedback loop of the controller have a negative impact on the performance. It is also shown that the asymmetry due to energy demand of different consumers to power plant increases the stability of the system.

Spatially extended systems can support local transient excitations in which just a part of the system is excited. The mechanisms reported so far are local excitability and excitation of a localized structure. Here we introduce an alternative mechanism based on the coexistence of two homogeneous stable states and spatial coupling. We show the existence of a threshold for perturbations of the homogeneous state. Subthreshold perturbations decay exponentially. Superthreshold perturbations induce the emergence of a long-lived structure formed by two back to back fronts that join the two homogeneous states. While in typical excitability the trajectory follows the remnants of a limit cycle, here reinjection is provided by front interaction, such that fronts slowly approach each other until eventually annihilating. This front-mediated mechanism shows that extended systems with no oscillatory regimes can display excitability., We acknowledge individual support (P.P.-R.) and project support (L.G.) by the Research Foundation - Flanders (Fonds Wetenschappelijk Onderzoek, FWO-Vlaanderen), by the IAP, and by the research council of the Vrije Universiteit Brussel (VUB). We also acknowledge financial support from Agencia Estatal de Investigación (AEI, Spain) and Fondo Europeo de Desarrollo Regional under Project ESoTECoS FIS2015-63628-C2-1-R (AEI/FEDER,UE).

This chapter presents the general theory about how different dissipative soliton (DS) dynamics are induced by inhomogeneities and drift. For this purpose, the prototypical Swift-Hohenberg equation (SHE) is used. The chapter focuses on the mechanism that leads to excitable dynamics. It discusses the modeling of fiber cavities in terms of the Lugiato-Lefever model, and describes the effect of periodic pumping in ring cavities. In fiber cavities and microresonators, inhomogeneities and drift are unavoidable due to imperfections in the fabrication process, material properties, and higher-order chromatic light dispersion. In the context of fiber cavities and microresonators, periodic boundary conditions lead to the emission of a train of solitons from the inhomogeneity. These trains of solitons lie at the basis of Kerr frequency comb generation. Therefore, the dynamical instabilities of cavity solitons induced by imperfections of themicroresonator can be particularly relevant for applications relying on stable frequency combs.

International audience; We consider an optoelectronic oscillator for ultra-pure microwave generation with two nonlinearly-coupled delay loops in which the output of one of the loops modulates the other. We introduce a suitable dynamical model and study the phase noise performance. Tuning the parameters of the second loop allows us to reduce the detrimental effect of the multiplicative phase noise and damp delay-induced spurious peaks. Also, nonlinear dynamics allows for stable microwave emission with larger amplitude than a single loop system.

We present a simple model for self-pulsation instability in passively phased high power optical fiber amplifier arrays with external feedback. Its key features are, first, the feedback level's sensitivity, and thus that of the cavity Q-value, to small phase changes of the array fields, and, second, the effect of refractive index nonlinearity in the amplifiers. The model's prediction of an instability threshold for arrays of at least two amplifiers is confirmed by a linearized stability analysis of a system in ring-cavity geometry, and the magnitudes of predicted power levels are well within the domain of recent experiments., This work was supported in part by the High Energy Laser Joint Technology Office (HELJTO) and the Air Force Office of Scientific Research (AFOSR).

8 pages, 15 figures., We analytically and numerically study the effect of an additional feedback in the semiconductor laser used to pump optoelectronic delay devices. We show that this additional feedback renders the system into chaotic regime for a broader parameter range and also induces a stronger chaotic behavior. We study the synchronization of this system as function of the parameter mismatch and show its capability for encoded message transmission., We gratefully thank Vasile Tronciu for helping us with the DDE-BIFTOOL program. As well, financial support from MICINN, Spain, and Feder under Project TEC2006-1009/MIC (PhoDECC) and Project FIS2004-00953 (CONOCE2) and by the EC Project PICASSO (IST-2005-34551) is acknowledged. R.M.Nguimdo also acknoledges the fellowship BES-2007-14627 under the FPI program of MICINN (Spanish Goverment).

6 pages, 8 figures.-- PDF pre-print., We study the effects of noise on excitable DS found on nonlinear Kerr cavities, showing that the system exhibits coherence resonance, characterized by a maximum degree of regularity for intermediate noise intensities. This behavior is observed for two different ways of applying noise: an additive white uncorrelated spatio-temporal noise and including fluctuations in the intensity of an addressing beam., We acknowledge financial support from MICINN (Spain) and FEDER through project FISICOS (FIS2007-60327).

7 pages, 8 figures., Several chaos encoding schemes codify the message in such a way that the mean value of the transmitted signal (carrier with the message) is different for bits “0” and “1”. We present a nonlinear filtering method that is able to detect very small changes in the mean value of a signal and therefore recover this kind of messages if its amplitude is larger than the chaotic fluctuations in the mean over the length of a bit.We also introduce a new codification method in which the mean value of the transmitted signal, over the length of each bit, is preserved and we show how it is able to beat the decryption scheme., This work was supported by MEC (Spain) and Feder under Projects TEC2006-1009/MIC (PhoDECC), TEC-2006-28105-E, and FIS2007-60327 (FISICOS); from EC Project PICASSO Grant IST-2005- 34551. The work of M. C. Soriano was supported by the MEC under a “Juan de la Cierva” contract.

The purpose of this paper is to analyze the propagation and the amplification of an input signal in networks of unidirectionally coupled micro-electro-mechanical systems (MEMS). Two types of external excitations are considered: sinusoidal and stochastic signals. We show that sinusoidal signals are amplified up to a saturation level which depends on the transmission rate and despite MEMS being nonlinear the sinusoidal shape is well preserved if the number of MEMS is not too large. However, increasing the number of MEMS, there is an instability that leads to chaotic behavior and which is triggered by the amplification of the harmonics generated by the nonlinearities. We also show that for stochastic input signals, the MEMS array acts as a band-pass filter and after just a few elements the signal has a narrow power spectra., The authors wish to acknowledge the support of the Humboldt Foundation (Germany) through the equipment grant.

We have reported in Phys. Rev. Lett. 110, 064103 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.064103 that in systems which otherwise do not show oscillatory dynamics, the interplay between pinning to a defect and pulling by drift allows the system to exhibit excitability and oscillations. Here we build on this work and present a detailed bifurcation analysis of the various dynamical instabilities that result from the competition between a pulling force generated by the drift and a pinning of the solitons to spatial defects. We show that oscillatory and excitable dynamics of dissipative solitons find their origin in multiple codimension-2 bifurcation points. Moreover, we demonstrate that the mechanisms leading to these dynamical regimes are generic for any system admitting dissipative solitons., This research was supported by the Research Foundation–Flanders (FWO-Vlaanderen), by the Junior Mobility Programme (JuMo) at KU Leuven, by the Belgian Science Policy Office (BelSPO) under Grant No. IAP 7-35, by the Research Council of the Vrije Universiteit Brussel, by the Ministerio de Economía y Competitividad (Spain) and Fondo Europeo de Desarrollo Regional under Grants Intense@Cosyp (FIS2012-30634) and TripHop (TEC2012-36335).

5 pages.-- Final full-text version of the paper available at: http://dx.doi.org/10.2529/PIERS060907134206., We characterize a scenario where localized structures in nonlinear optical cavities display an oscillatory behavior which becomes unstable leading to an excitable regime. Excitability emerges from spatial dependence since the system locally is not excitable. We show the existence of different mechanisms leading to excitability depending on the profile of the pump field., We acknowledge financial support from MEC (Spain) and FEDER: Grants BFM2001-0341-C02-02, FIS2004-00953 (CONOCE2) and FIS2004-05073-C04-03. AJ acknowledges financial support from the MEC.

We consider a model for two delay-coupled optoelectronic oscillators under positive delayed feedback as prototypical to study the conditions for synchronization of asymmetric square-wave oscillations, for which the duty cycle is not half of the period. We show that the scenario arising for positive feedback is much richer than with negative feedback. First, it allows for the coexistence of multiple in- and out-of-phase asymmetric periodic square waves for the same parameter values. Second, it is tunable: The period of all the square-wave periodic pulses can be tuned with the ratio of the delays, and the duty cycle of the asymmetric square waves can be changed with the offset phase while the total period remains constant. Finally, in addition to the multiple in- and out-of-phase periodic square waves, low-frequency periodic asymmetric solutions oscillating in phase may coexist for the same values of the parameters. Our analytical results are in agreement with numerical simulations and bifurcation diagrams obtained by using continuation techniques., This work benefited from the financial support of Ministerio de Economía y Competitividad (Spain) and Fondo Europeo de Desarrollo Regional under Projects No. FIS2012-30634 (INTENSE@COSYP) and No. TEC2012-36335 (TRIPHOP); European Social Fund and Govern de les Illes Balears under programs Grups Competitius and Formació de Personal Investigador; Fonds de la Recherche Scientifique-FNRS (Belgium); and the Belgian Science Policy Office under Grant No. IAP-7/35 “photonics@be.”

We show the coexistence of a fast-scale hyperchaos with a slow-scale periodic behavior in an integro-differential delayed dynamical system. This behavior arises after a sequence of Hopf bifurcations. This new phenomenology is experimentally evidenced with a Mach-Zehnder modulator optically fed by a semiconductor laser, and subjected to a delayed nonlinear electro-optical feedback. A “breathing” dynamics is therefore observed, consisting of ns-timescale hyperchaotic oscillations with a periodic modulation at a μs-timescale. A theoretical understanding of the phenomenon is also provided.

8 pages., We characterize the chaotic dynamics of semiconductor lasers subject to either optical or electro-optical feedback modeled by Lang-Kobayashi and Ikeda equations, respectively. This characterization is relevant for secure optical communications based on chaos encryption. In particular, for each system we compute as a function of tunable parameters the Lyapunov spectrum, Kaplan-Yorke dimension and Kolmogorov-Sinai entropy., This paper was supported in part from the Ministerio de Educacion y Ciencia (Spain) and FEDER Projects BFM2001-0341, TIC2001-4572-E, and FIS004–00953 and from the European Commission Project IST-2000-29683 OCCULT.

8 pages, 9 figures., We introduce and analyze a model for the dynamics of two coupled self-pulsating semiconductor lasers. We investigate the role of the complex coupling coefficient in the static and dynamic properties of the device. We find conditions for the emergence of coherent laser pulses, in which the two lasers display synchronous coherent self-pulsations (self-pulsating super-modes). Non-linear dynamics and two different routes to chaos are also individuated and discussed., This work was supported by the European Commission under VISTA HPRN-CT-2000-00034, under the OCCULT Project 2000- 29683, and by the Spanish MCyT under Project BFM2000-1108, MCyT and Feder SINFIBIO BFM 2001-0341-C02-02.

10 pages, 10 figures.-- Journal issue title proper: "Cryptography using optical chaos/Cryptographie par chaos optique". [EN] We review the main properties of two unidirectionally coupled single-mode semiconductor lasers (master-slave configuration). Our analysis is based on numerical simulations of a rate equations model. The emitter, or master laser, is assumed to be an external-cavity single-mode semiconductor laser subject to optical feedback that operates in a chaotic regime. The receiver, or slave laser, is similar to the emitter but can either operate in a chaotic regime, as the emitter (closed loop configuration), or without optical feedback and consequently under CW when it is uncoupled (open loop configuration). This configuration is one of the most simple and useful configuration for chaos based communication systems and data encryption. [FR] Les principales propriétés de couplage unidirectionnel entre deux laser à semiconducteurs monomodes (configuration maître-esclave) sont passées en revue. Cette analyse s'appuie sur des simulations numériques du modèle des équations d'évolution du laser à semiconducteur. L'émetteur, ou encore le laser maître, est constitué d'un laser semiconducteur monomode à cavité externe soumis à une contre-réaction optique, et fonctionnant en régime chaotique. Le récepteur, ou laser esclave, est semblable à l'émetteur, mais il peut fonctionner soit en régime chaotique comme l'émetteur (configuration en boucle fermée), soit sans contre-réaction optique (configuration en boucle ouverte), c'est-à-dire en régime continu lorsqu'il est non couplé. Cette dernière configuration est l'une des plus simples et des plus communes dans le contexte des systèmes de sécurisation des télécommunications optiques par chaos. This work was supported by the OCCULT project (IST-2000-29683) and the Spanish MCyT and FEDER projects CONOCE BFM2000-1108, SINFIBIO BMF2001-0341 and BFM2002-04369.