F. Tito Arecchi

Influence of observational noise on the recurrence quantification analysis

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 in nonlinear optics

Abstract 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.

Swarming Behavior in Plant Roots

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.

Chaotic spiking and incomplete homoclinic scenarios in semiconductor lasers with optoelectronic feedback

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.

Control of transient synchronization with external stimuli.

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.

Complexity versus Complex Systems: A New Approach to Scientific Discovery

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.

Introduction to Focus Issue: Nonlinear Dynamics in Cognitive and Neural Systems

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

Feature binding as neuron synchronization: quantum aspects

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 Plancks action.

Imaging and phase measurements of 3D objects at 10.6 microns by digital holography

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 CO2 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 CO2 laser sources in optical metrological applications.

Pattern competition in a high-power CO2 laser due to optogalvanic modulation of the pump profile

Experimental evidence of periodic alternation of different transverse modes in a high-power CO 2 laser is interpreted in terms of local cooling of the discharge column, which corresponds to the maximum emitted intensity. Optogalvanic coupling between emitted intensity and local discharge impedance values yields a transverse redistribution of discharge current and, hence, of laser gain. Thus, besides the fast feedback provided by the cavity, with high-power lasers one must account also for a slow global feedback because of the optogalvanic effects.