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Raw data for the article Emergence of disordered branching patterns in confined chiral nematic liquid crystals, Sources of funding: -ANID by Beca Doctorado Nacional 2020- 21201376. -ANID-Millenium Science Initiative Program–ICN17_012 (MIRO) -FONDECYT project 1210353 -FONDECYT project 11230941 -Universidad de Chile-VID project UI-015/22.

Self-organisation is a ubiquitous phenomenon in ecosystems. These systems can experience transitions from a uniform cover towards the formation of vegetation patterns as a result of symmetry-breaking instability. They can be either periodic or localised in space. Localised vegetation patterns consist of more or less circular spots or patches that can be either isolated or randomly distributed in space. We report on a striking patterning phenomenon consisting of localised vegetation labyrinths. This intriguing pattern is visible in satellite photographs taken in many territories of Africa and Australia. They consist of labyrinths which is spatially irregular pattern surrounded by either a homogeneous cover or a bare soil. The phenomenon is not specific to particular plants or soils. They are observed on strictly homogenous environmental conditions on flat landscapes, but they are also visible on hills. The spatial size of localized labyrinth ranges typically from a few hundred meters to ten kilometres. A simple modelling approach based on the interplay between short-range and long-range interactions governing plant communities or on the water dynamics explains the observations reported here., SCOPUS: ar.j, info:eu-repo/semantics/published

Multistable systems are characterized by exhibiting domain coexistence, where each domain accounts for the different equilibrium states. In case these systems are described by vectorial fields, domains can be connected through topological defects. Vortices are one of the most frequent and studied topological defect points. Optical vortices are equally relevant for their fundamental features as beams with topological features and their applications in image processing, telecommunications, optical tweezers, and quantum information. A natural source of optical vortices is the interaction of light beams with matter vortices in liquid crystal cells. The rhythms that govern the emergence of matter vortices due to fluctuations are not established. Here, we investigate the nucleation mechanisms of the matter vortices in liquid crystal cells and establish statistical laws that govern them. Based on a stochastic amplitude equation, the law for the number of nucleated vortices as a function of anisotropy, voltage, and noise level intensity is set. Experimental observations in a nematic liquid crystal cell with homeotropic anchoring and a negative anisotropic dielectric constant under the influence of a transversal electric field show a qualitative agreement with the theoretical findings.

Particle-type solutions are observed in out-of-equilibrium systems. These states can be motionless, oscillatory, or propagative depending on the injection and dissipation of energy. We investigate a family of localized standing waves based on a liquid-crystal light valve with spatiotemporal modulated optical feedback. These states are nonlinear waves in which energy concentrates in a localized and oscillatory manner. The organization of the family of solutions is characterized as a function of the applied voltage. Close to the reorientation transition, an amplitude equation allows us to elucidate the origin of these localized states and establish their bifurcation diagram. Theoretical findings are in qualitative agreement with experimental observations. Our results open the possibility of manipulating localized states induced by light, which can be used to expand and improve the storage and manipulation of information.

Modulation instability (MI) in the presence of noise typically leads to an irreversible and complete disintegration of a plane wave background. Here we report on experiments performed in a coherently driven nonlinear optical resonator that demonstrate nonlinear localization of dissipative MI: formation of persisting domains of MI-driven spatiotemporal chaos surrounded by a stable quasi-plane-wave background. The persisting localization ensues from a combination of bistability and complex spatiotemporal nonlinear dynamics that together permit a locally induced domain of MI to be pinned by a shallow modulation on the plane wave background. We further show that the localized domains of spatiotemporal chaos can be individually addressed---turned on and off at will---and we explore their transport behavior as the strength of the pinning is controlled. Our results reveal new fundamental dynamics at the interface of front dynamics and MI, and offer a route for tailored patterns of noiselike bursts of light.

Particle-type solutions are generic behaviors in out-of-equilibrium systems. These localized states are characterized by a discrete set of parameters such as position, width, and height. Even these solutions can have topological charges, localized vortices, which enriches the solutions and strengthens their respective stability. These solutions are characterized by exhibiting vorticity surrounded by a homogeneous state without vorticity. Frustrated chiral liquid crystals are a natural habitat for localized vortices, cholesteric bubbles. Here we study the emergence of chiral bubbles in the winding/unwinding transition of a chiral liquid crystal cell with homeotropic anchoring. Experimentally, we show that this winding/unwinding transition is subcritical in nature when one modifies the temperature, which also generates the emergence of spherulites through the contraction of cholesteric labyrinthine patterns. Theoretically, based on an amplitude equation inferred by symmetry arguments, we reveal the emergence of chiral bubbles from a cholesteric labyrinthine patterns.

We consider a two-dimensional array of heterogeneous nonlocally coupled phase oscillators on a flat torus and study the bound states of two counter-rotating spiral chimeras, shortly two-core spiral chimeras, observed in this system. In contrast to other known spiral chimeras with motionless incoherent cores, the two-core spiral chimeras typically show a drift motion. Due to this drift, their incoherent cores become spatially modulated and develop specific fingerprint patterns of varying synchrony levels. In the continuum limit of infinitely many oscillators, the two-core spiral chimeras can be studied using the Ott-Antonsen equation. Numerical analysis of this equation allows us to reveal the stability region of different spiral chimeras, which we group into three main classes---symmetric, asymmetric, and meandering spiral chimeras.

Cholesteric liquid crystals have attracted the scientific community's attention in the last decades due to the impressive textures displayed in various experiments. In particular, when varying the temperature of a cholesteric liquid crystal sample with homeotropic anchoring, complex textures arise, which resemble labyrinthine patterns built on the connections of the so-called cholesteric fingers. Near the winding/unwinding transition, we proposed a minimal phenomenological model that accounts for the first-order type transition and the symmetries in the system. At this transition, localized cholesteric fingers suffer a tip-splitting instability and the merging of pointed tips. We discuss the emergence of cholesteric labyrinths using experimental, analytical, and numerical techniques.

ANID-PFCHA Doctorado Nacional Grant 2017-21171672 ANID Millenium Science initiative program ICN17_012 Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT) CONICYT FONDECYT 1210353

Predicting complex nonlinear dynamical systems has been even more urgent because of the emergence of extreme events such as earthquakes, volcanic eruptions, extreme weather events (lightning, hurricanes/cyclones, blizzards, tornadoes), and giant oceanic rogue waves, to mention a few. The recent milestones in the machine learning framework offer a new prospect in this area [1] , [2] . For a high dimensional chaotic system, increasing the system’s size causes an augmentation of the complexity and, finally, more nodes in the network. Here, we propose a new supervised machine learning strategy to forecast bursts occurring in the turbulent regime of a fiber ring cavity. Indeed, we have recently demonstrated [3] that this system can continuously transform a stable periodic pattern with a well-defined frequency comb into a turbulent state via a spatiotemporal intermittency mechanism. Figure 1a ) shows an illustration of this transition. Even though a turbulent evolutions, an interesting feature is the persistent long-range correlation in the dynamics [3] . The system can then be seen as adjacent subdomains. Owing to this feature, instead of predicting the whole system, we use appropriate tools of chaos theory to identify recurrent picture in the past at the same location of the bursts. Figure 1b ) shows the statistics on the bursts (red) and the profiles detected at a previously computed time lag (blue). We have taken advantage of the apparent causality to make an association precursors-pulses. Knowing when and where the bursts may emerge, a fair question is " What is coming? ". On the other hand, as shown in Figure 1c ), no correlation can be found between the profile (amplitude and size) of the precursors of the corresponding pulse. However, using the pulses/precursors pairs to perform supervised learning with a recurrent neural network, we have obtained a high correlated map between the actual observation and the prediction, as can be seen in Figure 1d ). As our strategy deals with intrinsic characteristic quantities of the dynamical behavior, the pre-trained network can trigger the forecasting even for a more extensive system, provided that all the other parameters are the same.

Coupled oscillators can exhibit complex spatiotemporal dynamics. Here, we study the propagation of nonlinear waves into an unstable state in dissipative coupled oscillators. To this, we consider the dissipative Frenkel–Kontorova model, which accounts for a chain of coupled pendulums or Josephson junctions and coupling superconducting quantum interference devices. As a function of the dissipation parameter, the front that links the stable and unstable state is characterized by having a transition from monotonous to non-monotonous profile. In the conservative limit, these traveling nonlinear waves are unstable as a consequence of the energy released in the propagation. Traveling waves into unstable states are peculiar of dissipative coupling systems. When the coupling and the dissipation parameter are increased, the average front speed decreases. Based on an averaging method, we analytically determine the front speed. Numerical simulations show a quite fair agreement with the theoretical predictions. To show that our results are generic, we analyze a chain of coupled logistic equations. This model presents the predicted dynamics, opening the door to investigate a wider class of systems.

Driven nano-magnets have attracted increasing attention due to their potential applications and complex dynamical behavior. Spin valves are possibly the most studied driven nano-magnets because applied magnetic fields and electric currents can control their magnetization. Due to these properties, spin valves are proposed candidates for the new generation of memory units. Based on the Landau-Lifshitz-Gilbert-Slonczewski equation, we show that this system exhibits a wide range of magnetization textures, such as patterns, domain walls, and localized structures. Monitoring the Largest Lyapunov exponent, we demonstrate that these textures are chaotic. We numerically characterize the dynamical behavior of this device using the magnetic energy and the magnetoresistance. Finally, we present a phase diagram of the different types of spatial solutions as a function of the applied current and the field.

Machine learning algorithms have opened a breach in the fortress of the prediction of high-dimensional chaotic systems. Their ability to find hidden correlations in data can be exploited to perform model-free forecasting of spatiotemporal chaos and extreme events. However, the extensive feature of these evolutions constitutes a critical limitation for full-size forecasting processes. Hence, the main challenge for forecasting relevant events is to establish the set of pertinent information. Here, we identify precursors from the transfer entropy of the system and a deep Long Short-Term Memory network to forecast the complex dynamics of a system evolving in a high-dimensional spatiotemporal chaotic regime. Performances of this triggerable model-free prediction protocol based on the information flowing map are tested from experimental data originating from a passive resonator operating in such a complex nonlinear regime. We have been able to predict the occurrence of extreme events up to 9 round trips after the detection of precursor, i.e., 3 times the horizon provided by Lyapunov exponents, with 92 % of true positive predictions leading to 60 % of accuracy.

Small-sized systems exhibit a finite number of routes to chaos. However, in extended systems, not all routes to complex spatiotemporal behavior have been fully explored. Starting from the sine-Gordon model of parametrically driven chain of damped nonlinear oscillators, we investigate a route to spatiotemporal chaos emerging from standing waves. The route from the stationary to the chaotic state proceeds through quasiperiodic dynamics. The standing wave undergoes the onset of oscillatory instability, which subsequently exhibits a different critical frequency, from which the complexity originates. A suitable amplitude equation, valid close to the parametric resonance, makes it possible to produce universe results. The respective phase-space structure and bifurcation diagrams are produced in a numerical form. We characterize the relevant dynamical regimes by means of the largest Lyapunov exponent, the power spectrum, and the evolution of the total intensity of the wave field., to be published in Chaos, Solitons & Fractals

Chains of coupled oscillators exhibit energy propagation by means of waves, pulses, and fronts. Nonreciprocal coupling radically modifies the wave dynamics of chains. Based on a prototype model of nonlinear chains with nonreciprocal coupling to nearest neighbors, we study nonlinear wave dynamics. Nonreciprocal coupling induces a convective instability between unstable and stable equilibrium. Increasing the coupling level, the chain presents a propagative pattern, a traveling wave. This emergent phenomenon corresponds to the self-assembly of localized structures. The pattern wavelength is characterized as a function of the coupling. Analytically, the phase diagram is determined and agrees with numerical simulations.

Discrete dissipative coupled systems exhibit complex behavior such as chaos, spatiotemporal intermittence, chimera among others. We construct and investigate chimera states, in the form of confined stationary and dynamical states in a chain of parametrically driven sites with onsite damping and cubic nonlinearity. The system is modeled by the respective discrete parametrically driven damped nonlinear Schrodinger equation. Chimeras feature quasi-periodic or chaotic dynamic in the filled area, quantified by time dependence of the total norm (along with its power spectrum), and by the largest Lyapunov exponent. Systematic numerical simulations, in combination with some analytical results, reveal regions in the parameter space populated by stable localized states of different types. A phase transition from the stationary disorder states to spatially confined dynamical chaotic one is identified. Essential parameters of the system are the strength and detuning of the forcing, as well as the lattice's coupling constant., To be published in Chaos, Solitons and Fractals

We investigate the influence of the stimulated Raman scattering on the formation of bright and dark localized states in all-fiber resonators subject to a coherent optical injection, when operating in the normal dispersion regime. In the absence of the Raman effect, and far from any modulational instability, localized structures form due to the locking of domain walls connecting two coexisting continuous wave states, and undergo a particular bifurcation structure known as collapsed snaking. The stimulated Raman scattering breaks the reflection symmetry of the system, and modifies the dynamics, stability, and locking of domain walls. This modification leads to the formation of, not only dark, but also bright moving localized states, which otherwise are absent. We perform a detailed bifurcation analysis of these localized states, and classify their dynamics and stability as a function of the main parameters of the system.

Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT) CONICYT FONDECYT 1180903 Millennium Institute for Research in Optics (MIRO) ANID by Beca Doctorado Nacional 2020-21201376

This Focus Issue on instabilities and nonequilibrium structures includes invited contributions from leading researchers across many different fields. The issue was inspired in part by the "VII Instabilities and Nonequilibrium Structures 2019"conference that took place at the Pontifica Universidad Católica de Valparaiso, Chile in December 2019. The conference, which is devoted to nonlinear science, is one of the oldest conferences in South America (since December 1985). This session has an exceptional character since it coincides with the 80th anniversary of Professor Enrique Tirapegui. We take this opportunity to highlight Tirapegui's groundbreaking contributions in the field of random perturbations experienced by macroscopic systems and in the formation of spatiotemporal structures in such systems operating far from thermodynamic equilibrium. This issue addresses a cross-disciplinary area of research as can be witnessed by the diversity of systems considered from inert matter such as photonics, chemistry, and fluid dynamics, to biology., SCOPUS: re.j, info:eu-repo/semantics/published

The dynamics of ecological systems are often described by integrodifferential equations that incorporate nonlocal interactions associated with facilitative, competitive interactions between plants, and seed dispersion. In the weak-gradient limit, these models can be reduced to a simple partial-differential equation in the form of a nonvariational Swift–Hohenberg equation. In this contribution, we perform this reduction for any type of kernels provided that their Taylor series converge. Some parameters such as linear and nonlinear diffusion coefficients are affected by the spatial form of the kernel. In particular, Gaussian and exponential kernels are used to evaluate all coefficients of the reduced model. This weak gradient approximation is greatly useful for the investigation of periodic and localized vegetation patches, and gaps. Based on this simple model, we investigate the interaction between two-well separated patches and gaps. In the case of patches, the interaction is always repulsive. As a consequence, bounded states of patches are excluded. However, when two gaps are close to one another, they start to interact through their oscillatory tails. The interaction alternates between attractive and repulsive depending on the distance separating them. This allows for the stabilization of bounded gaps and clusters of them. The analytical formula of the interaction potential is derived for both patches and gaps interactions and checked by numerical investigation of the model equation. This volume is dedicated to Professor Ehud Meron on the occasion of his sixtieth birthday. We take this opportunity to express our warmest and most sincere wishes to him., SCOPUS: ar.j, info:eu-repo/semantics/published

We consider a generic interaction-redistribution model of vegetation dynamics to investigate the formation of patchy vegetation in semi-arid and arid landscapes. First, we perform a weakly nonlinear analysis in the neighborhood of the symmetry-breaking instability. Following this analysis, we construct the bifurcation diagram of the biomass density. The weakly nonlinear analysis allows us to establish the condition under which the transition from super- to subcritical symmetry-breaking instability takes place. Second, we generate a random distribution of localized patches of vegetation numerically. This behavior occurs in regimes where a bare state coexists with a uniform biomass density. Field observations allow to estimate the total biomass density and the range of facilitative and competitive interactions., SCOPUS: ar.j, info:eu-repo/semantics/published

The fronts are waves that connect two equilibria. The liquid crystals are no stranger to these phenomena. Front dynamics also was observed in other physical contexts, such as walls separating magnetic domains, fluidized granular states, chemical reactions, solidification, and combustion processes, and population dynamics, to mention a few. We find these phenomena in differents interface dynamics, as part of a robust phenomenon this ranging from chemistry and biology to physics. The propagation and dynamics of fronts depend on the nature of the states that are being connected. The invasion of a state into another is characterized usually by front propagation into unstable states. In the present work, we investigate the anisotropic front propagation close to phase transition SmA-N*. The bifurcation diagram shows a subcritical behavior, and the front speed is according to the mathematical model. A spatiotemporal diagram shows an evolution of the front with preferential direction.”

We investigate a vortex triplet induced by the combination of an electric and magnetic field onto a homeotropic nematic liquid crystal cell. The electric and magnetic fields are generated by two parallel electrodes and a magnetic ring, respectively. The vortex triplet remains stable and trapped at the center of the magnetic ring. Based on forcing the Ginzburg-Landau equation, valid close to the re-orientational transition, allow us to establish the origin of the vortex triplet. Numerical simulations show a quite fair agreement with theoretical findings and experimental observations.

We investigate topological states of matter in a system with injection and dissipation of energy. In an experiment involving a liquid crystal cell under the influence of a low frequency oscillatory electric field, we observe a transition from no vortex state to a state in which vortices persist. Depending on the period and the type of the forcing, the vortices self-organize forming square lattices, glassy states, and disordered vortex structures. Our results show that the matter maintained out of equilibrium by means of the temporal modulation of parameters can exhibit exotic states at room temperature.

International audience; Nonlinear pulse propagation is a major feature in continuously extended excitable systems. The persistence of this phenomenon in coupled excitable systems is expected. Here, we investigate theoretically the propagation of nonlinear pulses in a 1D array of evanescently coupled excitable semiconductor lasers. We show that the propagation of pulses is characterized by a hopping dynamics. The average pulse speed and bifurcation diagram are characterized as a function of the coupling strength between the lasers. Several instabilities are analyzed such as the onset and disappearance of pulse propagation, and a spontaneous breaking of the translation symmetry. The pulse propagation modes evidenced are specific to the discrete nature of the 1D array of excitable lasers. Linear oscillators coupled with springs to nearest neighbors exhibit wave propagation. This phenomenon is persistent when considering the continuous limit, i.e. when considering an elastic rope. In this limit, the wave dispersion relation is linear, unlike the discrete case of coupled systems where it is nonlinear. Here we study the propagation of localized nonlinear wave pulses in coupled excitable systems. Excitable oscillators play a fundamental role in understanding the activity of neurons, cardiac tissue, and oscillatory chemical reactions. Based on a model of a 1D array of excitable semiconductor lasers, we show that pulse propagation is characterized by a hopping dynamics and that it displays a rich variety of bifurcations. Counter-intuitively, we observe that pulses do not persist in the continuous limit.

A ring resonator made of a silica-based optical fiber is a paradigmatic system for the generation of dissipative localized structures or dissipative solitons. We analyze the effect of the non-instantaneous nonlinear response of the fused silica or the Raman response on the formation of localized structures. After reducing the generalized Lugiato-Lefever to a simple and generic bistable model with a nonlocal Raman effect, we investigate analytically the formation of moving temporal localized structures. This reduction is valid close to the nascent bistability regime, where the system undergoes a second-order critical point marking the onset of a hysteresis loop. The interaction between fronts allows for the stabilization of temporal localized structures. Without the Raman effect, moving temporal localized structures do not exist, as shown in M. G. Clerc, S. Coulibaly, and M. Tlidi, Phys. Rev. Res. 2, 013024 (2020). The detailed derivation of the speed and the width associated with these structures is presented. We characterize numerically in detail the bifurcation structure and stability associated with the moving temporal localized states. The numerical results of the governing equations are in close agreement with analytical predictions., SCOPUS: ar.j, info:eu-repo/semantics/published

International audience; Electrically driven nematic liquid crystals layers are ideal contexts for studying the interactions of local topological defects, umbilical defects. In homogeneous samples the number of defects is expected to decrease inversely proportional to time as a result of defect-pair interaction law, so-called coarsening process. Experimentally, we characterize the coarsening dynamics in samples containing glass beads as spacers and show that the inclusion of such imperfections changes the exponent of the coarsening law. Moreover, we demonstrate that beads that are slightly deformed alter the surrounding molecular distribution and attract vortices of both topological charges, thus, presenting a mainly quadrupolar behavior. Theoretically, based on a model of vortices diluted in a dipolar medium, a 2 3 exponent is inferred, which is consistent with the experimental observations.

Nonequilibrium systems exhibit particle-type solutions. Oscillons are one of the best-known localized states of systems with time-dependent forcing or parametrically driven systems. We investigate the transition from nonradiative to radiative oscillons in the parametrically driven sine-Gordon model in two spatial dimensions. The bifurcation takes place when the strength of the forcing (frequency) increases (decreases) above a certain threshold. As a result of this transition, the oscillon emits radially symmetric evanescent waves. Numerically, we provide the phase diagram and show the supercritical nature of this transition. For small oscillations, based on the amplitude equation approach, the sine-Gordon equation with time-dependent forcing is transformed into the parametrically driven damped nonlinear Schrödinger model in two spatial dimensions. This amplitude equation exhibits a transition between nonradiative to radiative localized structures, consistently. Both models show quite good agreement.

Mobility properties of spatially localized structures arising from chaotic but deterministic forcing of the bistable Swift-Hohenberg equation are studied and compared with the corresponding results when the chaotic forcing is replaced by white noise. Short structures are shown to possess greater mobility, resulting in larger root-mean-square speeds but shorter displacements than longer structures. Averaged over realizations, the displacement of the structure is ballistic at short times but diffusive at larger times. Similar results hold in two spatial dimensions. The effects of chaotic forcing on the stability of these structures is also quantified. Shorter structures are found to be more fragile than longer ones, and their stability region can be displaced outside the pinning region for constant forcing. Outside the stability region the deterministic fluctuations lead either to the destruction of the structure or to its gradual growth.

Fragmentation followed by desertification in water-limited resources and/or nutrient-poor ecosystems is a major risk to the biological productivity of vegetation. By using the vegetation interaction-redistribution model, we analyse the interaction between localised vegetation patches. Here we show analytically and numerically that the interaction between two or more patches is always repulsive. As a consequence, only a single localised vegetation patch is stable, and other localised bounded states or clusters of them are unstable. Following this, we discuss the impact of the repulsive nature of the interaction on the formation and the selection of vegetation patterns in fragmented ecosystems., SCOPUS: ar.j, info:eu-repo/semantics/published

Nonuniform spatial distributions of vegetation in scarce environments consist of either gaps, bands often called tiger bush or patches that can be either self-organized or spatially localized in space. When the level of aridity is increased, the uniform vegetation cover develops localized regions of lower biomass. These spatial structures are generically called vegetation gaps. They are embedded in a uniform vegetation cover. The spatial distribution of vegetation gaps can be either periodic or randomly distributed. We investigate the combined influence of the facilitative and the competitive nonlocal interactions between plants, and the role of crow/root allometry, on the formation of gapped vegetation patterns. We characterize first the formation of the periodic distribution of gaps by drawing their bifurcation diagram. We then characterize localized and aperiodic distributions of vegetation gaps in terms of their snaking bifurcation diagram., SCOPUS: ar.j, info:eu-repo/semantics/published

In ordinary consciousness, noise is associated with the term “hindrance”; it is considered as a nuisance that can lead to communication or signal transmission failure or prevent the detection of a weak signal to be measured. However, under certain conditions the impact of noise can be counter-intuitively a resource. In nonlinear systems, noise can induce novel regimes leading to the formation of synchronized structures, coherence between the output and the input of resonators or even to the amplification of weak signals. In other words, noise can play a constructive role, with potential benefits for signal processing or measurement for instance. Single or coupled Nano-Opto-ElectroMechanical resonators whose design is based on suspended photonic crystal membrane could be used as a toy-system to pursue two main goals: stochastic amplification and chaos. As such noise-aided processes might have a strong impact in noise-assisted applications including signal processing or sensing.

Matter under different equilibrium conditions of pressure and temperature exhibits different states such as solid, liquid, gas, and plasma. Exotic states of matter, such as Bose–Einstein condensates, superfluidity, chiral magnets, superconductivity, and liquid crystalline blue phases are observed in thermodynamic equilibrium. Rather than being a result of an aggregation of matter, their emergence is due to a change of a topological state of the system. These topological states can persist out of thermodynamics equilibrium. Here we investigate topological states of matter in a system with injection and dissipation of energy by means of oscillatory forcing. In an experiment involving a liquid crystal cell under the influence of a low-frequency oscillatory electric field, we observe a transition from a non-vortex state to a state in which vortices persist, topological transition. Depending on the period and the type of the forcing, the vortices self-organise, forming square lattices, glassy states, and disordered vortex structures. The bifurcation diagram is characterised experimentally. A continuous topological transition is observed for the sawtooth and square forcings. The scenario changes dramatically for sinusoidal forcing where the topological transition is discontinuous, which is accompanied by serial transitions between square and glassy vortex lattices. Based on a stochastic amplitude equation, we recognise the origin of the transition as the balance between stochastic creation and deterministic annihilation of vortices. Numerical simulations show topological transitions and the emergence of square vortex lattice. Our results show that the matter maintained out of equilibrium by means of the temporal modulation of parameters can exhibit exotic states.

We show analytically and numerically that time-delayed nonlocal response induces traveling localized states in bistable systems. These states result from the interaction of fronts between homogeneous steady states. We illustrate this mechanism by considering an experimentally relevant system - the fiber cavity with the noninstantaneous Raman response. Close to the nascent bistability, we performed a derivation of a generic bistable model with a nonlocal delayed response. Analytical expressions of the width and the speed of traveling localized states are derived. Without a time-delayed nonlocal response, traveling localized states are excluded. In addition, we propose realistic parameters and perform numerical simulations of the governing model equation., SCOPUS: ar.j, info:eu-repo/semantics/published

International audience; We review experimental and theoretical results on the computing properties of single spiking micropillar lasers and present numerical studies of propagation and computing in chains of evanescently coupled micropillar lasers. Single mi-cropillar lasers are shown to behave as ultrafast optical neurons with sub-nanosecond spike times. They also possess absolute and relative refractory times, spike latency and show temporal summation. With delayed optical feedback, they emulate an autapse. These basic neural properties can be used for simple photonic computing. We show by numerical simulations of a chain of coupled spiking micropillar lasers that basic logical operations can be implemented in photonic circuits, as well as temporal pattern recognition based on the collision properties of pulses in this chain.

A pair of periodically coupled and forced simple oscillators can exhibit aperiodic behaviors. Here we study the effect of periodic spatial modulations in an optical dimer composed of photorefractive saturable waveguides. The propagation of light along these waveguides as a function of the initial condition exhibits chaotic behaviors. The dynamical behaviors are elucidated based on the adequate representation of the variables, frequency spectra, and Poincare sections. Homoclinic and heteroclinic entanglements associated with the hyperbolic points that separate the stable equilibria are the origin of the chaotic behavior. The different dynamical regimes have been characterized as a function of light power and initial conditions. Our results open the possibility of using optical saturable dimers in the secure transmission of information.

The use of dye-doped liquid crystals allows the amplification of the coupling of light and liquid crystals. Light can induce the self-organization of the molecular order. The appearance of ring patterns has been observed, which has been associated with phase modulation. However, the morphology and dynamics of the ring patterns are not consistent with self-modulation. Based on an experimental setup with two parallel coherence beams orthogonal to a liquid crystal cell, one of which induces photo-isomerization and the other causes illumination, the formation of ring patterns is studied. To use these two coherent beams, we synthesize methylred methyl ester as a dye-dopant, which is photosensitive only to one of the light beams, and a commercial E7 liquid crystal as a matrix. Based on a mathematical model that accounts for the coupling between the concentration of the cis-state and the order parameter, we elucidate the emergence of the rings as forming patterns in an inhomogeneous medium. The bifurcation diagram is analytically characterized. The emergence, propagation of the rings, and the establishment of the ring patterns are in fair agreement with the experimental observations.