Emergence of spike correlations in periodically forced excitable systems

In sensory neurons the presence of noise can facilitate the detection of weak information-carrying signals, which are encoded and transmitted via correlated sequences of spikes. Here we investigate relative temporal order in spike sequences induced by a subthreshold periodic input, in the presence of white Gaussian noise. To simulate the spikes, we use the FitzHugh-Nagumo model, and to investigate the output sequence of inter-spike intervals (ISIs), we use the symbolic method of ordinal analysis. We find different types of relative temporal order, in the form of preferred ordinal patterns which depend on both, the strength of the noise and the period of the input signal. We also demonstrate a resonance-like behavior, as certain periods and noise levels enhance temporal ordering in the ISI sequence, maximizing the probability of the preferred patterns. Our findings could be relevant for understanding the mechanisms underlying temporal coding, by which single sensory neurons represent in spike sequences the information about weak periodic stimuli

Extreme intensity pulses in a semiconductor laser with a short external cavity

We present a numerical study of the pulses displayed by a semiconductor laser with optical feedback in the short cavity regime, such that the external cavity round trip time is smaller than the laser relaxation oscillation period. For certain parameters there are occasional pulses, which are high enough to be considered extreme events. We characterize the bifurcation scenario that gives rise to such extreme pulses and study the influence of noise. We demonstrate intermittency when the extreme pulses appear and hysteresis when the attractor that sustains these pulses is destroyed. We also show that this scenario is robust under the inclusion of noise

Analysis of noise-induced temporal correlations in neuronal spike sequences

This is a copy of the author 's final draft version of an article published in the journal European physical journal. Special topics. The final publication is available at Springer via http://dx.doi.org/10.1140/epjst/e2016-60024-6We investigate temporal correlations in sequences of noise-induced neuronal spikes, using a symbolic method of time-series analysis. We focus on the sequence of time-intervals between consecutive spikes (inter-spike-intervals, ISIs). The analysis method, known as ordinal analysis, transforms the ISI sequence into a sequence of ordinal patterns (OPs), which are defined in terms of the relative ordering of consecutive ISIs. The ISI sequences are obtained from extensive simulations of two neuron models (FitzHugh-Nagumo, FHN, and integrate-and-fire, IF), with correlated noise. We find that, as the noise strength increases, temporal order gradually emerges, revealed by the existence of more frequent ordinal patterns in the ISI sequence. While in the FHN model the most frequent OP depends on the noise strength, in the IF model it is independent of the noise strength. In both models, the correlation time of the noise affects the OP probabilities but does not modify the most probable pattern.Peer ReviewedPostprint (author's final draft

Inverse Anticipating Synchronization

We report a new type of chaos synchronization:inverse anticipating synchronization, where a time delay chaotic system can drive another system in such a way that the driven system anticipates the driver by synchronizing with its inverse future state. We extend the concept of inverse anticipating chaos synchronization to cascaded systems. We propose means for the experimental observation of inverse anticipating chaos synchronization in external cavity lasers.Comment: LaTex 6 pages, resubmitted to PR

Steady-state stabilization due to random delays in maps with self-feedback loops and in globally delayed-coupled maps

We study the stability of the fixed-point solution of an array of mutually coupled logistic maps, focusing on the influence of the delay times, $\tau_{ij}$, of the interaction between the $i$th and $j$th maps. Two of us recently reported [Phys. Rev. Lett. {\bf 94}, 134102 (2005)] that if $\tau_{ij}$ are random enough the array synchronizes in a spatially homogeneous steady state. Here we study this behavior by comparing the dynamics of a map of an array of $N$ delayed-coupled maps with the dynamics of a map with $N$ self-feedback delayed loops. If $N$ is sufficiently large, the dynamics of a map of the array is similar to the dynamics of a map with self-feedback loops with the same delay times. Several delayed loops stabilize the fixed point, when the delays are not the same; however, the distribution of delays plays a key role: if the delays are all odd a periodic orbit (and not the fixed point) is stabilized. We present a linear stability analysis and apply some mathematical theorems that explain the numerical results.Comment: 14 pages, 13 figures, important changes (title changed, discussion, figures, and references added

Extreme intensity pulses in a semiconductor laser with a short external cavity

We present a numerical study of the pulses displayed by a semiconductor laser with optical feedback in the short-cavity regime, such that the external cavity round-trip time is shorter than the laser relaxation oscillation period. For certain parameters there are occasional pulses, which are high enough to be considered extreme events. We characterize the bifurcation scenario that gives rise to such extreme pulses and study the influence of noise. We demonstrate intermittency when the extreme pulses appear and hysteresis when the attractor that sustains these pulses is destroyed. We also show that this scenario is robust under the inclusion of noise. © 2013 American Physical Society.This work was supported in part by Grant No. FA8655-12-1-2140 from EOARD US, Grant No. FIS2012-37655-C02-01 from the Spanish MCI, and Grant No. 2009 SGR 1168 from the Generalitat de Catalunya. C. Masoller acknowledges support from the ICREA Academia programe. J.Z.M. acknowledges support from FISICOS Grant No. FIS2007-60327 of the Spanish MCI and INTENSE@COSYP Grant No. FIS2012-30634 of the FEDER. J.A.R. acknowledges support from Grant No. BES-2008-003398 and thanks the UPC for hospitality during his visit, during which part of this work was done.Peer Reviewe

Comparison of two types of synchronization of external-cavity semiconductor lasers

Missatge de l'editorial: "This paper was published in Optical letters and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-27-1-31. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law."We study numerically the synchronization of external-cavity semiconductor lasers in a master–slave configuration, based on a Lang–Kobayashi-type model. Depending on the feedback and coupling strengths, the slave laser synchronizes with the injected optical field or with the injected field but lags in time. We show that these two types of synchronization present different robustness with respect to the noise, frequency detuning, and current modulation of the master laser.Peer ReviewedPostprint (published version

Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: Theory and experiment

We analyze the dynamics of two semiconductor lasers with so-called orthogonal time-delayed mutual coupling: the dominant TE (x) modes of each laser are rotated by 90∘ (therefore, TM polarization or y) before being coupled to the other laser. Although this laser system allows for steady-state emission in either one or in both polarization modes, it may also exhibit stable time-periodic dynamics including square waveforms. A theoretical mapping of the switching dynamics unveils the region in parameter space where one expects to observe long-term time-periodic mode switching. Detailed numerical simulations illustrate the role played by the coupling strength, the mode frequency detuning, or the mode gain to loss difference. We complement our theoretical study with several experiments and measurements. We present time series and intensity spectra associated with the characteristics of the square waves and other waveforms observed as a function of the strength of the delay coupling. The experimental observations are in very good agreement with the analysis and the numerical results.Peer ReviewedPostprint (published version

Complex transitions to synchronization in delay-coupled networks of logistic maps

A network of delay-coupled logistic maps exhibits two different synchronization regimes, depending on the distribution of the coupling delay times. When the delays are homogeneous throughout the network, the network synchronizes to a time-dependent state [Atay et al., Phys. Rev. Lett. 92, 144101 (2004)], which may be periodic or chaotic depending on the delay; when the delays are sufficiently heterogeneous, the synchronization proceeds to a steady-state, which is unstable for the uncoupled map [Masoller and Marti, Phys. Rev. Lett. 94, 134102 (2005)]. Here we characterize the transition from time-dependent to steady-state synchronization as the width of the delay distribution increases. We also compare the two transitions to synchronization as the coupling strength increases. We use transition probabilities calculated via symbolic analysis and ordinal patterns. We find that, as the coupling strength increases, before the onset of steady-state synchronization the network splits into two clusters which are in anti-phase relation with each other. On the other hand, with increasing delay heterogeneity, no cluster formation is seen at the onset of steady-state synchronization; however, a rather complex unsynchronized state is detected, revealed by a diversity of transition probabilities in the network nodes

Parameter and coupling estimation in small groups of Izhikevich neurons

Nowadays, experimental techniques allow scientists to have access to large amounts of data. In order to obtain reliable information from the complex systems which produce these data, appropriate analysis tools are needed}. The Kalman filter is a {frequently used} technique to infer, assuming a model of the system, the parameters of the model from uncertain observations. A well-known implementation of the Kalman filter, the Unscented Kalman filter (UKF), was recently shown to be able to infer the connectivity of a set of coupled chaotic oscillators. {I}n this work, we test whether the UKF can also reconstruct the connectivity of {small groups of} coupled neurons when their links are either electrical or chemical {synapses}. {In particular, w}e consider Izhikevich neurons, and aim to infer which neurons influence each other, considering {simulated spike trains as the experimental observations used by the UKF}. First, we {verify} that the UKF can recover the parameters of a single neuron, even when the parameters vary in time. Second, we analyze small neural ensembles and}} demonstrate that the UKF allows inferring the connectivity between the neurons, even for heterogeneous, directed, and {temporally evolving} networks. {Our results show that time-dependent parameter and coupling estimation is possible in this nonlinearly coupled system