Experimental Observation of Coherence and Stochastic Resonances in an Electronic Chua Circuit

Stochastic and coherence resonances appear in nonlinear systems subjected to an external source of noise and are characterized by a maximum response at the optimal value of the noise intensity. This paper shows experimentally that it is possible to observe them in a chaotic system. To this end we have analysed an electronic Chua circuit running in the chaotic regime and added noise to its dynamics. In the case of coherence resonance, we observe an optimal periodicity for the jumps between chaotic attractors, whereas in the case of stochastic resonance we observe a maximum in the signal-to-noise ratio at the frequency of an external sinusoidal perturbation.Comment: 6 page

Synchronization of Chaotic Systems by Common Random Forcing

We show two examples of noise--induced synchronization. We study a 1-d map and the Lorenz systems, both in the chaotic region. For each system we give numerical evidence that the addition of a (common) random noise, of large enough intensity, to different trajectories which start from different initial conditions, leads eventually to the perfect synchronization of the trajectories. The largest Lyapunov exponent becomes negative due to the presence of the noise terms.Comment: 5 pages, uses aipproc.cls and aipproc.sty (included). Five double figures are provided as ten separate gif files. Version with (large) postscript figures included available from http://www.imedea.uib.es/PhysDept/publicationsDB/date.htm

Anticipating the response of excitable systems driven by random forcing

We study the regime of anticipated synchronization in unidirectionally coupled model neurons subject to a common external aperiodic forcing that makes their behavior unpredictable. We show numerically and by implementation in analog hardware electronic circuits that, under appropriate coupling conditions, the pulses fired by the slave neuron anticipate (i.e. predict) the pulses fired by the master neuron. This anticipated synchronization occurs even when the common external forcing is white noise.Comment: 12 pages (RevTex format

Coherence and synchronization in diode-laser arrays with delayed global coupling

The dynamics of a semiconductor-laser array whose individual elements are coupled in a global way through an external mirror is numerically analysed. A coherent in-phase solution is seen to be preferred by the system at intermediate values of the feedback coupling strength. At low values of this parameter, a strong amplification of the spontaneous emission noise is observed. A tendency towards chaos synchronization is also observed at large values of the feedback strength.Comment: 8 pages, LaTeX, 6 PS figures, to appear in International Journal of Bifurcation and Chao

Diversity-induced resonance

We present conclusive evidence showing that different sources of diversity, such as those represented by quenched disorder or noise, can induce a resonant collective behavior in an ensemble of coupled bistable or excitable systems. Our analytical and numerical results show that when such systems are subjected to an external subthreshold signal, their response is optimized for an intermediate value of the diversity. These findings show that intrinsic diversity might have a constructive role and suggest that natural systems might profit from their diversity in order to optimize the response to an external stimulus.Comment: 4 pages, 3 figure

Chaos-Based Optical Communications: Encryption Versus Nonlinear Filtering

7 pages, 8 figures.Several chaos encoding schemes codify the message in such a way that the mean value of the transmitted signal (carrier with the message) is different for bits “0” and “1”. We present a nonlinear filtering method that is able to detect very small changes in the mean value of a signal and therefore recover this kind of messages if its amplitude is larger than the chaotic fluctuations in the mean over the length of a bit.We also introduce a new codification method in which the mean value of the transmitted signal, over the length of each bit, is preserved and we show how it is able to beat the decryption scheme.This work was supported by MEC (Spain) and Feder under Projects TEC2006-1009/MIC (PhoDECC), TEC-2006-28105-E, and FIS2007-60327 (FISICOS); from EC Project PICASSO Grant IST-2005- 34551. The work of M. C. Soriano was supported by the MEC under a “Juan de la Cierva” contract.Peer reviewe

Coherence Resonance in Chaotic Systems

We show that it is possible for chaotic systems to display the main features of coherence resonance. In particular, we show that a Chua model, operating in a chaotic regime and in the presence of noise, can exhibit oscillations whose regularity is optimal for some intermediate value of the noise intensity. We find that the power spectrum of the signal develops a peak at finite frequency at intermediate values of the noise. These are all signatures of coherence resonance. We also experimentally study a Chua circuit and corroborate the above simulation results. Finally, we analyze a simple model composed of two separate limit cycles which still exhibits coherence resonance, and show that its behavior is qualitatively similar to that of the chaotic Chua systemComment: 4 pages (including 4 figures) LaTeX fil

Permutation-information-theory approach to unveil delay dynamics from time-series analysis

PACS: 05.45.Tp, 89.70.Cf, 02.30.KsIn this paper a novel approach to identify delay phenomena from time series is developed. We show that it is possible to perform a reliable time delay identification by using quantifiers derived from information theory, more precisely, permutation entropy and permutation statistical complexity. These quantifiers show clear extrema when the embedding delay of the symbolic reconstruction matches the characteristic time delay of the system. Numerical data originating from a time delay system based on the well-known Mackey-Glass equations operating in the chaotic regime were used as test beds. We show that our method is straightforward to apply and robust to additive observational and dynamical noise. Moreover, we find that the identification of the time delay is even more efficient in a noise environment. Our permutation approach is also able to recover the time delay in systems with low feedback rate or high nonlinearity.We thank Dr. L. Pesquera for very useful discussions and comments on the current research. L.Z. and O.A.R. were supported by Consejo Nacional de Investigaciones Científi- cas y Técnicas CONICET , Argentina. The work of M.C.S. was supported by MEC Spain under a “Juan de la Cierva” contract. O.A.R. is supported by PVE of CAPES, Brazil. Part of this work was funded by MEC Spain , MICINN Spain , and FEDER under Projects No. TEC2006-10009/MIC PhoDeCC , No. TEC2009-14101 DeCoDicA , and No. FIS2007-60327 FISICOS , and by the EC Project PHOCUS, European Commission FET-Open Grant No. 24076Peer reviewe