Showing papers by "Stefano Boccaletti published in 1994"

Adaptive Recognition of a Chaotic Dynamics

Abstract: The local variation rates of a chaotic dynamical system provide a means of stroboscopic observation at adjustable times which minimize the second variation of the coordinates. The sequence of strobing intervals carries global information on the dynamics, yielding a suitable indicator which discriminates deterministic from stochastic signals. Due to the adaptive nature of the strobing process, the characterization of this indicator requires a computational effort much smaller than statistical methods.

Adaptive recognition of chaos

Abstract: We exploit the information provided by the local variation rates of a chaotic dynamical system, to introduce a stroboscopic observation at adjustable times at which the system displays a regular geometry. The sequence of strobing intervals yields suitable indicators which discriminate deterministic from stochastic signals. The evaluation of these indicators requires a computational effort much smaller than statistical methods.

Pattern formation and competition in photorefractive oscillators.

Abstract: We introduce a general model of pattern formation in optical systems made of a cavity with an active medium as a photorefractive crystal fed by a pump. The model is based on the interplay of a diffractive equation for the optical field and a diffusive equation for the medium refractivity. The aim of the model is to describe a series of experiments which have shown mode competition (periodic or chaotic alternation) for low Fresnel numbers (F) and mode coexistence, leading to short range space correlations, for high F. For low F, a linear stability analysis provides the set of modes above threshold as a function of the transverse wave number. Due to the interplay of the optical and the diffusive interactions, different behaviors result depending on the thickness of the medium as compared to the optical absorption length and diffusion length. Including the leading nonlinearities compatible with the symmetry constraints, we introduce normal form equations which describe the time‐dependent mode competition. In the case of a large number of modes (high F), nonlinear mode–mode interaction is equivalent to a self‐induced noise. In this limit, the relevant feature to be compared with the experiment is the power spectrum.

Modeling excitable media by a one variable cellular automaton: Application to the cardiac case.

Abstract: The dynamics of an assembly of cardiac cells is modeled by a simple cellular automaton that reduces to a single variable the two variable competition of the standard models of excitable media. Furthermore, a short superexcitability period is introduced, as suggested by the dynamics of the single cardiac miocyte. The model reproduces several pathological cardiac behaviors as, e.g., the fast transition from normal behavior to fibrillation, showing how this latter one can either occur over the whole spatial domain or can be confined within a limited region.

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

Abstract: 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.

Mutually recursive method to detect and remove noise in chaotic dynamics

Abstract: Many papers have been published recently about the characterization of time-dependent processes through techniques using wavelet approach. Our work takes into account a particular class of time-dependent processes in nonlinear realm. We want to characterize chaotic dynamics from the standpoint of its unstable periodicities. For this aim we introduce a new technique able to stabilize such unstable orbits. We illustrate this technique both from the theoretical and the experimental standpoint. As a further step, we want to deal with the problem of detecting and removing noise from chaotic dynamics. In this paper, firstly, we show how our technique is able to distinguish with very high sensitivity between a purely chaotic dynamics and a chaotic dynamics with noise even though the noise percentage is very low (of the order of 1 percent only Secondly, we apply our technique to remove noise from this dynamics. Finally, we compare both from the theoretical and experimental standpoint our technique with the well known wavelet technique. This work is a part of 'Skynnet' international project supported by the Italian National Institute for Nuclear Physics (INFN) and partially devoted to the application of new chaotic techniques instantiated in neural architectures for compressing, storing and transmitting information to earth from satellites.

Boundary dominated versus bulk dominated regime in optical space-time complexity

Abstract: By increasing the aspect ratio of an optical cavity with a photorefractive crystal, we observe the transition from a boundary-controlled regime, where the size of the transverse patterns scales with the aspect ratio, to a bulk-controlled regime where the pattern size is independent of the aspect ratio. In this new regime, the size corresponds to an intrinsic correlation length imposed by diffusion processes within the material. Such a new behavior is explained by the wave-number dependence of the gain within the instability region. Model equations provide good agreement with the two asymptotic cases of small aspect ratio (diffraction limited regime) and large aspect ratio (diffusion limited regime).