E. Allaria

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.

Digital holography at 10.6 μm

Digital holography (DH) at the 10.6 l mo f aC O 2 laser can be successfully used to reconstruct numerically intensity and phase of the object wavefield. A Mach–Zehnder interferometer with a pyroelectric type optoelectronic sensor array is used to record digital off-axis Fresnel holograms of an extended object. We demonstrate that, although the pyrocamera spatial resolution is much less than that of typical detectors working in the visible spectral region, good intensity and phase reconstructions are provided. The principle of Fresnel reconstruction in DH is described and results of reconstruction process for object size of the order of 700 lm are presented and discussed. Furthermore we propose a method to accurately determine the wave vector components of the reference wavefield for off-axis DH set-up to obtain correct phase wavefield reconstruction. 2002 Elsevier Science B.V. All rights reserved.

Numerical and experimental exploration of phase control of chaos

A well-known method to suppress chaos in a periodically forced chaotic system is to add a harmonic perturbation. The phase control of chaos scheme uses the phase difference between a small added harmonic perturbation and the main driving to suppress chaos, leading the system to different periodic orbits. Using the Duffing oscillator as a paradigm, we present here an in-depth study of this technique. A thorough numerical exploration has been made focused in the important role played by the phase, from which new interesting patterns in parameter space have appeared. On the other hand, our novel experimental implementation of phase control in an electronic circuit confirms both the well-known features of this method and the new ones detected numerically. All this may help in future implementations of phase control of chaos, which is globally confirmed here to be robust and easy to implement experimentally.

Propensity criterion for networking in an array of coupled chaotic systems.

We examine the mutual synchronization of a one-dimensional chain of chaotic identical objects in the presence of a stimulus applied to the first site. We first describe the characteristics of the local elements, and then the process whereby a global nontrivial behavior emerges. A propensity criterion for networking is introduced, consisting in the coexistence within the attractor of a localized chaotic region, which displays high sensitivity to external stimuli, and an island of stability, which provides a reliable coupling signal to the neighbors in the chain. Based on this criterion, we compare homoclinic chaos, recently explored in lasers and conjectured to be typical of a single neuron, with Lorenz chaos.

Transient polarization dynamics in a CO2 laser

Abstract We study experimentally and theoretically the polarization alternation during the switch-on transient of a quasi-isotropic CO 2 laser emitting on the fundamental mode. The observed transient dynamics is well reproduced by means of a model which provides a quantitative discrimination between the intrinsic asymmetry due to the kinetic coupling of molecules with different angular momenta, and the extrinsic anisotropies, due to a tilted intracavity window. Furthermore, the experiment provides a numerical assignment for the decay rate of the coherence term for a CO 2 laser.

In phase and antiphase synchronization of coupled homoclinic chaotic oscillators.

We numerically investigate the dynamics of a closed chain of unidirectionally coupled oscillators in a regime of homoclinic chaos. The emerging synchronization regimes show analogies with the experimental behavior of a single chaotic laser subjected to a delayed feedback.

Homoclinic chaos in a laser: synchronization and its implications in biological systems

Phase synchronization of a CO2 laser with feedback, exhibiting homoclinic chaos, is realized by a tiny periodic perturbation of a control parameter. The deviations of the modulation frequency from the optimal one induce phase slips, thus yielding an imperfect phase synchronization. Based on the information of these phase slips, the modulation frequency can be readjusted until the phase slips are eliminated. In this way, a control loop which detects the phase slips provides an adaptive tracking of the natural frequency of the dynamical system. Moreover, we have shown that the system’s susceptibility is largest when a periodic impulsive perturbation is applied near the saddle focus. r 2002 Published by Elsevier Science Ltd.

Comparison of single neuron models in terms of synchronization propensity

A plausible model for coherent perception is the synchronization of chaotically distributed neural spike trains over wide cortical areas. A recently introduced propensity criterion provides a tool for a quantitative comparison of different neuron models in terms of their ability to synchronize to an applied perturbation. We explore the propensity of several systems and indicate the requirements to be satisfied by a plausible candidate for modeling neuronal activity. Our results show that the conflicting requirements of stability and sensitivity leading to high propensity to synchronization can be satisfied by a strongly nonuniform attractor made of two distinct regions: a saddle focus plus a sufficiently separated saddle node.

Negative hysteresis in a laser with modulated parameters

Abstract The negative hysteresis at low frequencies (less than 10 Hz) is observed in a CO2 laser with modulated discharge current. The origin of this phenomenon is found in an additional loss modulation which can appear due to the heating of intracavity elements by laser radiation. The results of numerical simulations on the base of the complex laser model are in a good agreement with experimental results.

Controlling transient dynamics to communicate with homoclinic chaos

A control that stabilizes the transient dynamics of a homoclinic chaotic laser is used to encode discrete sources of information. The controlled trajectory is a complex spiking signal that has a constrained interspike interval, and therefore, the ratio of information transmitted is approximately constant. We also show that the controlled signal that encodes the source contains more information than the source. This property is advantageously used to correct possible errors in the transmission, or to increase the ratio of information per transmitted spike.