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International audience; We revisit the model of the laser with feedback and the minimal nonlinearity leading to chaos. Although the model has its origin in laser physics, with peculiarities related to the [Formula: see text] laser, it belongs to the class of the three-dimensional paradigmatic nonlinear oscillator models giving chaos. The proposed model contains three key nonlinearities, two of which are of the type [Formula: see text], where [Formula: see text] and [Formula: see text] are the fast and slow variables. The third one is of the type [Formula: see text], where [Formula: see text] is an intermediate feedback variable. We analytically demonstrate that it is essential for producing chaos via local or global homoclinic bifurcations. Its electronic implementation in the range of kilo Hertz region confirms its potential in describing phenomena evolving on different time scales.

A communication scheme based on the synchronization of two chaotic quantum dot light emitting diodes (QD-LEDs) is theoretically examined. The Chaos in the QD-LED is generated by means of an optical feedback. Synchronization of the chaos is achieved by varying coupling strength between the transmitter and the receiver as unidirectional coupling. The proposed communication schemes is test a by successfully transmitting messages.

We present an experimental investigation of the complex dynamics of a modulated relaxation oscillator implemented by using a unipolar junction transistor (UJT) showing the transition to chaos through torus breakdown. In a previous paper a continuous model was introduced for the same system, explaining chaos based on analogy with a memristor. We propose here a new approach based on a piecewise linear model with delay considering a measured parasitic delay effect. The inclusion of this delay, accounting for memory effects, increases the dimensionality of the model, allowing the transition to chaos as observed in the experiment. The piecewise delayed model shows analogies with a two-dimensional leaky integrate-and-fire model used in neurodynamics.

We present a series of experiments to demonstrate digital holography on reflective objects at wavelength 10.6 μm of a CO 2 laser using a pyrocam array. Fresnel holograms of reflective objects are recorded by a Mach–Zehnder interferometer. We describe a method for improving the accuracy of the numerical reconstructions and for compensating the loss of resolution at longer wavelength by Fresnel reconstruction of digitally recorded infrared holograms.

By tuning a control parameter, a chaotic system can either display two or more attractors (generalized multistability) or exhibit an interior crisis, whereby a chaotic attractor suddenly expands to include the region of an unstable orbit (bursting regime). Recently, control of multistability and bursting have been experimentally proved in a modulated class B laser by means of a feedback method. In a bistable regime, the method relies on the knowledge of the frequency components of the two attractors. Near an interior crisis, the method requires retrieval of the unstable orbit colliding with the chaotic attractor. We also show that a suitable parameter modulation is able to control bistability in the Lorenz system. We observe that, for every given modulation frequency, the chaotic attractor is destroyed under a boundary crisis. The threshold control amplitude depends on the control frequency and the location of the operating point in the bistable regime. Beyond the boundary crisis, the system remains in the steady state even if the control is switched off, demonstrating control of bistability.

Feature binding denotes how a large collection of coupled neurons combines external signals with internal memories into new coherent patterns of meaning. An external stimulus spreads over an assembly of coupled neurons, building up a corresponding collective state. Thus, the synchronization of spike trains of many individual neurons is the basis of a coherent perception. Homoclinic chaos has been proposed as the most suitable way to code information in time by trains of equal spikes occurring at apparently erratic times; a new quantitative indicator, called propensity, is introduced to select the most appropriate neuron model. In order to classify the set of different perceptions, the percept space is given a metric structure. The distance in percept space is conjugate to the duration of the perception in the sense that an uncertainty relation in percept space is associated with time limited perceptions. Thus coding of different percepts by synchronized spike trains entails fundamental quantum features with a quantum constant related to the details of the perceptual chain and very different from Planck's action.

Pattern formation and competition occur in a nonlinear extended medium if dissipation allows for attracting sets, independently of initial and boundary conditions. This intrinsic patterning emerges from a reaction diffusion dynamics (Turing chemical patterns). In optics, the coupling of an electromagnetic field to a polarizable medium and the presence of losses induce a more general (diffraction-diffusion) mechanism of pattern formation. The presence of a coherent phase propagation may lead to a large set of unstable bands and hence to a richer variety with respect to the chemical case. A review of different experimental situations is presented, including a discussion on suitable indicators which characterize the different regimes. Vistas on perspective new phenomena and applications include an extension to atom optics.

The FitzHugh-Nagumo neurons driven by a periodic forcing undergo a period-doubling route to chaos and a transition to mixed-mode oscillations. When coupled, their dynamics tend to be synchronized. We show that the chaotically spiking neurons change their internal dynamics to subthreshold oscillations, the phenomenon referred to as firing death. These dynamical changes are observed below the critical coupling strength at which the transition to full chaotic synchronization occurs. Moreover, we find various dynamical regimes in the subthreshold oscillations, namely, regular, quasiperiodic, and chaotic states. We show numerically that these dynamical states may coexist with large-amplitude spiking regimes and that this coexistence is characterized by riddled basins of attraction. The reported results are obtained for neurons implemented in the electronic circuits as well as for the model equations. Finally, we comment on the possible scenarios where the coupling-induced firing death could play an important role in biological systems. DOI: 10.1103/PhysRevE.87.022919

The synchronization in four forced FitzHugh-Nagumo (FHN) systems is studied, both experimentally and by numerical simulations of a model. We show that synchronization may be achieved either by coupling of systems through bidirectional diffusive interactions, by introducing a common noise to all systems or by combining both ingredients, noise and coupling together. Here we consider white and colored noises, showing that the colored noise is more efficient in synchronizing the systems respect to white noise. Moreover, a small addition of common noise allows the synchronization to occur at smaller values of the coupling strength. When the diffusive coupling in the absence of noise is considered, the system undergoes the transition to subthreshold oscillations, giving a spike suppression regime. We show that noise destroys the appearance of this dynamical regime induced by coupling. (C) 2012 Elsevier B.V. All rights reserved.

There was an error in the funding statement. The correct funding statement is: "This work was supported by Marie Curie European Reintegration Grant N. 239324 MIPAN (Memory and information processing in assemblies of neurons) within the 7th European Community Framework Program, http://cordis.europa.eu/fp7/dc/index.cfm [^] (MC), Ente Cassa di Risparmio di Firenze, URL:http://www.entecarifirenze.it/ [^] (SM) and EU ERC Project N. 227878 COLLMOT (Complex structure and dynamics of collective motion), http://erc.europa.eu/ [^] (TV). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript."

Long wavelength interferometry has been widely applied in different fields, such as infrared optics, infrared transmitting materials, high-reflective multilayer dielectric coatings for highpower laser systems. In optical metrology, long-wave interferometers are also employed for shape measurement of reflective rough surfaces and for testing optical systems that requires deep aspherics. An advantage of using longer wavelength is that the aspheric departure from the best fit reference-sphere, in unit of the probing wavelength, is reduced at longer wavelength, thus allowing one to obtain an interferogram of the deep aspheric under test. This leads to extension of the unambiguous distance measurement range, a well-known problem in interferometric metrology, where the essential difficulty relates to the interferometric fringe order, which cannot be determined unambiguously from a single measurement of phase interference. This problem is also of particular significance in digital holographic and interferomety based applications where digital processing of the recorded interferogram makes it possible to extract quantitatively amplitude and phase of the numerically reconstructed wavefront (Cuche el al., 1999a, 1999b; Vest, 1979; Yaroslavsky & Eden, 1996). Digital holography based imaging techniques provide real time capabilities to record also three-dimensional objects using interference between an object wave and a reference wave captured by an image sensor such a CCD sensor. Three-dimensional 3D information of the object can be obtained from the numerical reconstruction of a single digitally recorded hologram, since the information about the optically interfering waves is stored in the form of matrices. The numerical reconstruction process offers many more possibilities than conventional optical processing (Goodman & Lawrence, 1967; Stetson & Powell, 1966; Stetson & Brohinsky, 1985). For example, it is possible to numerically focus on any section of the three dimensional volume object without mechanical focusing adjustment (Grilli et al., 2001; Lai et al., 2000), correct optical components defects such as lens aberrations or compensate the limited depth of field of an high magnification microscope objective. Full digital processing of holograms requires high spatial resolution sensor arrays with demanding capabilities for imaging applications and non destructive testing. In this regard, several new recording materials and optoelectronic sensors have been devised for

We present experimental and numerical evidence of control and synchronization of burst events in modulated CO(2) lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model display the frequency locking of bursts in a suitable interval of coupling strengths. The analogy with neuronal bursting will also be discussed in view of the role of bursting synchronization in cognitive functions.

Digital holography in the mid infrared range is shown to be a feasible technique for optical metrological applications. The technique allows to reconstruct both amplitude and phase of wavefronts scattered by a 3D object. Experimental results of the method applied to the reconstruction of digitally holograms recorded at CO 2 laser wavelength of 10.6 micron are reported. It is show that good reconstructions can be obtained even with the lower spatial resolution of IR recording detectors compared to visible CCD array. The results show that new prospective can be exploited by using high power CO 2 laser sources in optical metrological applications.

We present experimental and numerical evidence of synchronization of burst events in two different modulated ${\mathrm{CO}}_{2}$ lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling.

An approach is presented for the reconstruction of phase synchronization phenomena in a chaotic CO2 laser from experimental data. We analyze this laser system in a regime able to phase synchronize with a weak sinusoidal forcing. Our technique recovers the synchronization diagram of the experimental system from only few measurement data sets, thus allowing the prediction of the regime of phase synchronization as well as nonsynchronization in a broad parameter space of forcing frequency and amplitude without further experiments.

A novel approach is presented for the reconstruction of phase synchronization phenomena in a chaotic CO2 laser from experimental data. We analyze this laser system in a regime of homoclinic chaos, which is able to phase synchronize with a weak sinusoidal forcing. Our technique recovers the synchronization diagram of the experimental system from only few measurement data sets, thus allowing the prediction of the regime of phase synchronization as well as non‐synchronization in a broad parameter space of forcing frequency and amplitude without further experiments.

The current understanding of complexity in computer science is that it corresponds to how the amount of computational resources invested in solving a problem scales with the system size. On the contrary, in natural sciences, a complex system is such that its knowledge cannot be confined to a unique model, but it is stratified over different and mutually irreducible hierarchical levels, each one with its own rules and language [1].

Given a system with a limited number of degrees of freedom, together with its interaction with the environment; can one evaluate a critical time (decoherence time) within which the system behaves fully quantum mechanically (including Einstein-Podolsky-Rosen (EPR)—entanglements), and after which it displays quasi-classical features? And if the system is isolated, but its classical limit displays chaotic behavior, would this be a sufficient replacement for the environment? A general positive answer to these questions would settle many open issues.

Interactions between individuals that are guided by simple rules can generate swarming behavior. Swarming behavior has been observed in many groups of organisms, including humans, and recent research has revealed that plants also demonstrate social behavior based on mutual interaction with other individuals. However, this behavior has not previously been analyzed in the context of swarming. Here, we show that roots can be influenced by their neighbors to induce a tendency to align the directions of their growth. In the apparently noisy patterns formed by growing roots, episodic alignments are observed as the roots grow close to each other. These events are incompatible with the statistics of purely random growth. We present experimental results and a theoretical model that describes the growth of maize roots in terms of swarming.

We demonstrate experimentally and theoretically the existence of slow chaotic spiking sequences in the dynamics of a semiconductor laser with ac-coupled optoelectronic feedback. The timescale of these dynamics is fully determined by the high-pass filter in the feedback loop and their erratic, though deterministic, nature is evidenced by means of the interspike interval (ISI) probability distribution. We eventually show that this regime is the result of an incomplete homoclinic scenario to a saddle-focus, where an exact homoclinic connection does not occur.

A network of coupled chaotic oscillators can switch spontaneously to a state of collective synchronization at some critical coupling strength. We show that for a locally coupled network of units with coexisting quiescence and chaotic spiking states, set slightly below the critical coupling value, the collective excitable or bistable states of synchronization arise in response to a stimulus applied to a single node. We provide an explanation of this behavior and show that it is due to a combination of the dynamical properties of a single node and the coupling topology. By the use of entropy as a collective indicator, we present a new method for controlling the transient synchronization.

This is a short review of the investigations done at Istituto Nazionale di Ottica on the onset of deterministic chaos in single mode, homogeneous line lasers. While carrying these researches, we discovered that bistabilty (or more generally multistability) is common to most nonlinear dynamical systems, that is, usually there are many coexisting attractors for the same control parameters. In such bistable (or multistable) situations, addition of a small amount of noise yields long memory effects displaying low frequency spectra of 1/f type. A theory of these effects is outlined.