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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.

This research reports a theoretical investigation on the role of filtered optical feedback (FOF) in the quantum dot light emitting diode (QD-LED). The underlying dynamics is affected by a sidle node, which returns to an elliptical shape when the wetting layer (WL) is neglected. Both filter width and time delay change the appearance of different dynamics (chaotic and mixed mode oscillations ,MMOs). The results agrees with the experimental observations. Here, the fixed point analysis for QDs was done for the first time. For QD-LED with FOF, the system transits from the coherence collapse (CC) case in conventional optical feedback (COF) to a coherent case with a filtered mode in FOF. It was found that the WL washes out the modes which is an unexpected result. This may attributed to the longer capture time of WL compared with that between QD states. Thus, WL reduces the chaotic behavior.

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.

At the borderline between neuroscience and physics of complex phenomena, a new paradigm is under investigation, namely feature binding. This terminology 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. Based on recent investigations, a novel conjecture for the dynamics of single neurons and, consequently, for neuron assemblies has been formulated. Homoclinic chaos is 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 by introducing a distance measure between distinct percepts. 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. It is conjectured that they are related to the details of the perceptual chain rather than depending on Planck's action.)

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.

In this paper, we estimate the errors due to observational noise on the recurrence quantification analysis (RQA). Based on this estimation, we present ways to minimize these errors. We give a criterion to choose the threshold e needed for the optimal computation of the recurrence plot (RP). One important point is to show the limits of interpretability of the results of the RQA if it is applied to measured time series. We show that even though the RQA is very susceptible to observational noise, it can yield reliable results for an optimal choice of e if the noise level is not too high. We apply the results to typical models, such as white noise, the logistic map and the Lorenz system, and to experimental laser data.

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

We show that the chaotically spiking neurons coupled in a ring configuration changes 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. We find various dynamical regimes in the subthreshold oscillations, namely, regular, quasi-periodic 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. Moreover, we show that under a particular coupling configuration, the neural network exhibits bistability between two configurations of clusters. Each cluster composed of two neurons undergoes independent chaotic spiking dynamics. As an appropriate external perturbation is applied to the system, the network undergoes changes in the clusters configuration, involving different neurons at each time. We hypothesize that the winning cluster of neurons, responsible for perception, is that exhibiting higher mean frequency. The clusters features may contribute to an increase of local field potential in the neural network. The reported results are obtained for neurons implemented in the electronic circuits as well as for the model equations.

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.

When an ambiguous stimulus is observed, our percep- tion undergoes dynamical changes between two states, a situation extensively explored in association with the Necker cube. Such phenomenon refers to bistable per- ception. Here, we present a model neural network composed of forced FitzHugh-Nagumo neurons, im- plemented also experimentally in an electronic circuit. We show, that under a particular coupling configu- ration, the neural network exhibit bistability between two configurations of clusters. Each cluster composed of two neurons undergoes independent chaotic spiking dynamics. As an appropriate external perturbation is applied to the system, the network undergoes changes in the clusters configuration, involving different neu- rons at each time. We hypothesize that the winning cluster of neurons, responsible for perception, is that exhibiting higher mean frequency. The clusters fea- tures may contribute to an increase of local field po- tential in the neural network.

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 explore two different moments of human cognition, namely apprehension (A), whereby a coherent perception emerges by recruitment of large neuron groups and judgment (B), whereby memory retrieval of different (A) units coded in a suitable language and comparison of them leads to the formulation of a judgment. The first one has a duration around 1 sec (from 0.5 to 3 sec), it appears as an a-temporal present and its neural correlate is a wide synchronization in the EEG gamma band. It may be described as an interpretation of sensorial stimuli in terms of some stored algorithm, via a Bayes procedure. The second one entails the comparison of two apprehensions acquired at different times, coded in a given language, and retrieved by memory. It lasts around 3 sec and requires self-consciousness, as the judging agent must be well aware that he/she is the same one who faces the two coded apprehensions under scrutiny in order to extract a mutual relation. At variance with (A), (B) does not presuppose an algorithm, but it rather builds a new behavioural model by an inverse Bayes procedure. It will be shown how this build up of a novel model is related to creativity and free will.

Synchronization phenomena have been the subject of intense studies since their first observation by Huygens in pendulum clocks. The subsequent discovery of deterministic chaos introduced a new kind of an oscillating system, a chaotic oscillator. In the late 1980s researchers turned their attention to the synchronization properties of chaotic systems (1–4), occurring when two, or more, chaotic oscillators are coupled, or, in case of the unidirectional synchronization, when a chaotic oscillator (master) drives another chaotic oscillator (slave). Despite their unpredictable nature, whose most remarkable feature is the exponential divergence of trajectories starting with infinitely close initial conditions, synchronization of chaotic systems is a phenomenon well established experimentally and reasonably understood theoretically. The increasing interest in chaotic synchronization is motivated by its potential applications. Clear understanding of these phenomena and the dynamical mechanisms behind them opens new opportunities for applications in different fields of science. In biology, for instance, a challenging problem is to understand how a group of cells or functional units, each displaying complicated behavior, can interact with one another to produce a coherent response on a higher organizational level. In secure communications, a message can be hidden in the output of a chaotic system during transmission and can be recovered by using a copy of the original system, synchronized to the first (5). In this context, the investigation has been focused on chaotic optoelectonic devices. Within the variety of dynamical regimes observed in semiconductor devices, chaotically spiking attractors play a special role. Typical time traces consist of large pulses separated by irregular time intervals in which the system displays small-amplitude chaotic oscillations. These erratic –though fully deterministic– sequences of pulses, mimic the dynamics experimentally observed in neurons (6) and many hypothesis have been done on their role in neural information processing (see (7) and references therein). Therefore, experiments Optoelectronic Feedback in Semiconductor Light Sources: Optimization of Network Components for Synchronization 29

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.

A scientific problem described within a given code is mapped by a corresponding computational problem, We call complexity (algorithmic) the bit length of the shortest instruction which solves the problem. Deterministic chaos in general affects a dynamical systems making the corresponding problem experimentally and computationally heavy, since one must reset the initial conditions at a rate higher than that of information loss (Kolmogorov entropy). One can control chaos by adding to the system new degrees of freedom (information swapping: information lost by chaos is replaced by that arising from the new degrees of freedom). This implies a change of code, or a new augmented model. Within a single code, changing hypotheses is equivalent to fixing different sets of control parameters, each with a different a-priori probability, to be then confirmed and transformed to an a-posteriori probability via Bayes theorem. Sequential application of Bayes rule is nothing else than the Darwinian strategy in evolutionary biology. The sequence is a steepest ascent algorithm, which stops once maximum probability has been reached. At this point the hypothesis exploration stops. By changing code (and hence the set of relevant variables) one can start again to formulate new classes of hypotheses . We call semantic complexity the number of accessible scientific codes, or models, that describe a situation. It is however a fuzzy concept, in so far as this number changes due to interaction of the operator with the system under investigation. These considerations are illustrated with reference to a cognitive task, starting from synchronization of neuron arrays in a perceptual area and tracing the putative path toward a model building.

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.

Homoclinic chaos implies the recurrent return of the dynamical trajectory to a saddle focus, in whose neighbourhood the system susceptibility (response to an external perturbation) is very high and hence it is very easy to lock to an external stimulus. Thus homoclinic chaos appears as the easiest way to encode information in time by a code consisting of trains of equal spikes occurring at erratic times. Based on recent laboratory investigations of homoclinic chaotic systems, and how they mutually synchronize by weak coupling, a novel conjecture on the dynamics of the single neuron is formulated. The central issue of cognitive science is how a large collection of coupled neurons combines external data with internal memories into new coherent patterns of meaning. Such a process is called “feature binding”, insofar as the coherent patterns combine together features which are extracted separately by specialized cells, but which do not make sense as isolated items. A powerful conjecture, with experimental confirmation, is that feature binding in perceptual tasks implies the mutual synchronization of axonal spike trains in neurons which can be far away and yet contribute to a well defined perception by sharing the same sequence. Thus we use our expertise in arraying a large number of homoclinic chaotic nodes into a synchronized network as a laboratory model of the brain behavior.

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.

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.

Heteroclinic chaos (HC) implies the recurrent return of the dynamical trajectory to a saddle focus (SF) in whose neighborhood the system response to an external perturbation is very high and hence it is very easy to lock to an external stimulus. Thus HC appears as the easiest way to encode information in time by a train of equal spikes occurring at erratic times. Implementing such a dynamics with a single mode CO2 laser with feedback, we have a heteroclinic connection between the SF and a saddle node (SN) whose role it to regularize the phase space orbit away from SF. Due to these two different fixed points, the laser intensity displays identical spikes separated by erratic ISIs (interspike intervals). Such a dynamics is highly prone to spike‐synchronization, either by an external signal or by mutual interaction in a network of identical systems. Applications to communication and noise induced synchronization will be reported. In experimental neuroscience a recent finding is that feature binding ,that is, combination of external stimuli with internal memories into new coherent patterns of meaning, implies the mutual synchronization of axonal spike trains in neurons which can be far away and yet share the same sequence. Several dynamical systems have been proposed to model such a behavior. We introduce a measurable parameter, namely, the synchronization “propensity”. Propensity is the amount of synchronization achieved in a chaotic system by a small sinusoidal perturbation of a control parameter. It is very low for coupled Lorenz or FitzHugh‐Nagumo chains. It displays isolated peaks for the Hindmarsh‐Rose model, showing that this is a convenient description of the bursting behavior typical of neurons in the CPG (central pattern generator) system. Instead, HC shows a high propensity over a wide input frequency range, demonstrating that it is the most convenient model for semantic neurons.

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].

Homoclinic spike trains have been intensively investigated for single mode C02 lasers [1]; however, their occurrence has a more general significance insofar as this scenario fits the main aspects of action potentials in neurons.Stabilizing homoclinic trains has therefore a relevance for neural communication and synchronization, which seems to be the universal time code for perceptions. The core dynamics of homoclinic chaos is represented by the passage through a saddle point, in which neighbourhood the system susceptibility (response to an external perturbation) is veryhigh [21 and hence it is very easy to apply a control [1• A few aspects of regularization of homoclinic chaos are covered, such as, synchronization by an external pace-maker [4], DSS (delayed self-synchronization) [5], bursting [6],and MS (noise induced synchronization) [7]. Such a general scenario is compared with specific neurodynamic models;moreover its impact on communicating with chaos is discussed [8].Homoclinic chaos of the Shilnikov type, initially observed in laser experiments [1], shows striking similarities with theelectrical spike trains traveling on the axons of animal neurons [9]. More generally, chemical oscillators based on anactivator-inhibitor competition, which rule biological clocks controlling living rhythms, such as the heart pacemaker,hormone production, metabolism etc., are subject to frequency fluctuations of homoclinic type, since in general theycan not be reduced to a two dimensional dynamics, as done in artificial clocks in order to have stable limit cycles[2].Experimental evidence of synchronization on a laser operating in a homoclinic chaos regime is provided by adding asmall periodic modulation of a control parameter. Take a single mode CO2 laser with an intracavity electro-optic lossmodulator, driven by the voltage of a detector exposed to the laser intensity; the voltage passes through an amplifier ofgain R an it is summed to a fixed bias voltage B.The two control parameters (R and B) are set in a region where the laser intensity shows homoclinic chaos. The laserintensity displays a large spike above zero followed by a fast damped train of a few oscillations and a successive longer

The chaotic spike train of a homoclinic dynamical system is self-synchronized by applying a time delayed correction proportional to the laser output intensity. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long periodic orbits is possible. On these orbits, the dynamics appears chaotic over a finite time, but then it repeats with a recurrence time that is slightly longer than the delay time. The effect, called delayed self-synchronization (DSS), displays analogies with neurodynamic events which occur in the build-up of long term memories.

In this work we describe a simple method of encoding in real time information in the inter-spike intervals of a homoclinic chaotic system. This has been experimentally tested by means of an instantaneous synchronization between the laser intensity of a CO 2 laser with feedback in the regime of homoclinic chaos and an external pulsed signal of very low power. The information is previously encoded in the temporal intervals between consecutive pulses of the external signal. The value of the inter-pulse intervals is varied each time a new pulse is generated. ( Summary only available )

Extraction of quantitative features from observations via measuring devices M means that the words of science are coded as numbers, and the syntaxis is a set of mathematical rules, thus all consequences should be worked in a purely deductive way. This characteristic of science displays two orders of drawbacks, namely, undecidability of deductive procedures, and intractability of complex situations. The way out of such a crisis consists in a frequent readjustment of M suggested by the observed events. This adaptive strategy differs from the adaptivity of a learning machine, which — inputted by a data stream — readjusts itself over a class of theoretical explanations in order to select the optimal choice. On the contrary, the scientist not only modifies the explanations for a fixed data set, but also explores different data sets by modifying M, that is, by selecting a different point of view. This M-adjustment is a pre-linguistic operation, not expressible by a formal language. Hence, the scientific endeavor can not be reduced to a machine task.

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.

By increasing the Fresnel number of F of a ring cavity with photorefractive gain, the transition from a low F regime, where few modes compete in a regular or irregular sequence, to a high F regime, where many modes oscillate simultaneously giving rise to spatio-temporal chaos is shown. The transverse field is characterized by an increasing number of topological defects, whose mean separation is related to the spatial correlation length of the field.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

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.

Coherence is a long range order absent at thermal equilibrium, where a system is the superposition of many uncorrelated components. To build non-trivial correlations, the system must enter a nonlinear dynamical regime. The nonlinearity leads to a multiplicity of equilibrium states, the number of which increases exponentially with the number of partners; we call complexity such a situation. Complete exploration of complexity would require a very large amount of time. On the contrary, in cognitive tasks, one reaches a decision within a few hundred milliseconds. Neuron synchronization lasting around 301 msec is the indicator of a conscious perception (Gestalt); however, the loss of information in the chaotic spike train of a single neuron takes a few msec, thus a conscious perception implies a control of chaos, whereby the information stored in a brain area survives for a time sufficient to elicit an action. Control of chaos is achieved by the interaction of a bottom-up stimulus with a top-down control (induced by the semantic memory). We call creativity this optimal control of neuronal chaos; it goes beyond the Bayesian inference, which is the way a computer operates, thus it represent a non-algorithmic step.

In this Focus Issue, two interrelated concepts, namely, deterministic chaos and cognitive abilities, are discussed.

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.

A scientific problem described within a given code is mapped by a corresponding computational problem. We call (algorithmic) complexity the bit length of the shortest instruction which solves the problem. Deterministic chaos in general affects a dynamical system making the corresponding problem experimentally and computationally heavy, since one must reset the initial conditions at a rate higher than that of information loss (Kolmogorov entropy). One can control chaos by adding to the system new degrees of freedom (information swapping: information lost by chaos is replaced by that arising from the new degrees of freedom). This implies a change of code, or a new augmented model. Within a single code, changing hypotheses is equivalent to fixing different sets of control parameters, each with a different a-priori probability, to be then confirmed and transformed to an a-posteriori probability via Bayes theorem. Sequential application of Bayes rule is nothing else than the Darwinian strategy in evolutionary biology. The sequence is a steepest ascent algorithm, which stops once maximum probability has been reached. At this point the hypothesis exploration stops.By changing code (and hence the set of relevant variables) one can start again to formulate new classes of hypotheses. We call creativity the action of code changing, which is guided by hints not formalized within the previous code, whence not accessible to a computer. We call semantic complexity the number of different scientific codes, or models, that describe a situation. It is however a fuzzy concept, in so far as this number changes due to interaction of the operator with the context.These considerations are illustrated with reference to a cognitive task, starting from synchronization of neuron arrays in a perceptual area and tracing the putative path towards a model building. Since this is a report on work in progress, we skip technicalities in order to stress the gist of the question, and provide references to more detailed work.

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.

A photodetector, coupled to a computer via an AC-DC converter (capacity 8 or 12 bit) is used to monitor the time changes in daylight illumination. In particular, a picture of the successive (percent) changes in lighting is given by averaging input data across pre-established time blocks, to refer to "frequencies" of importance from the biological stand point. This assessment of the instability of lighting, on a fine time scale, might be of importance for those systems, like human vision (and, why not, robotic vision), working on a differential sensitivity basis, and where the input is controlled by servomechanisms.