arXiv subjects

C. Masoller

Publications and source records attributed to C. Masoller.

18 recordsLinked to original sources

arXiv2025

Bubbling in Oscillator Networks

A network of coupled time-varying systems, where individual nodes are interconnected through links, is a modeling framework widely used by many disciplines. For identical nodes displaying a complex behavior known as chaos, clusters of nodes or the entire network can synchronize for a range of coupling strengths. Here, we demonstrate that small differences in the nodes give rise to desynchronization events, known as bubbling, in regimes where synchronization is expected. Thus, small unit heterogeneity in all real systems has an unexpected and outsized effect on the network dynamics. We present a theoretical analysis of bubbling in chaotic oscillator networks and predict when bubble-free behavior is expected. Our work demonstrates that the domain of network synchronization is much smaller than expected and is replaced by epochs of synchronization interspersed with extreme events. Our findings have important implications for real-world systems where synchronized behavior is crucial for system functionality.

nlin.CD↗

arXiv2024

Quantifying wave propagation in a chain of FitzHugh-Nagumo neurons

Understanding how external stimuli propagate in neural systems is an important challenge in the fields of neuroscience and nonlinear dynamics. Despite extensive studies over several decades, this problem remains poorly understood. In this work, we examine a simple ``toy model'' of an excitable medium, a linear chain of diffusely coupled FitzHugh-Nagumo neurons, and analyze the transmission of a sinusoidal signal injected into one of the neurons at the ends of the chain. We measure to what extent the propagation of the wave reaching the opposite end is affected by the frequency and amplitude of the signal, the number of neurons in the chain and the strength of their mutual diffusive coupling. To quantify these effects, we measure the cross-correlation between the time-series of the membrane potentials of the end neurons. This measure allows us to detect the values of the parameters that delimit different propagation regimes.

q-bio.NC↗

arXiv2023

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.

q-bio.NC↗

arXiv2021

Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks

Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones, and how to quantify nonlinear and/or high-order temporal correlations. Here we propose a new technique to reliably address both problems. Our approach follows two steps: first, we train an artificial neural network (ANN) with flicker (colored) noise to predict the value of the parameter, $\alpha$, that determines the strength of the correlation of the noise. To predict $\alpha$ the ANN input features are a set of probabilities that are extracted from the time series by using symbolic ordinal analysis. Then, we input to the trained ANN the probabilities extracted from the time series of interest, and analyze the ANN output. We find that the $\alpha$ value returned by the ANN is informative of the temporal correlations present in the time series. To distinguish between stochastic and chaotic signals, we exploit the fact that the difference between the permutation entropy (PE) of a given time series and the PE of flicker noise with the same $\alpha$ parameter is small when the time series is stochastic, but it is large when the time series is chaotic. We validate our technique by analysing synthetic and empirical time series whose nature is well established. We also demonstrate the robustness of our approach with respect to the length of the time series and to the level of noise. We expect that our algorithm, which is freely available, will be very useful to the community.

physics.data-an↗

arXiv2021

Network diffusion capacity unveiled by dynamical paths

Improving the understanding of diffusive processes in networks with complex topologies is one of the main challenges of today's complexity science. Each network possesses an intrinsic diffusive potential that depends on its structural connectivity. However, the diffusion of a process depends not only on this topological potential but also on the dynamical process itself. Quantifying this potential will allow the design of more efficient systems in which it is necessary either to weaken or to enhance diffusion. Here we introduce a measure, the {\em diffusion capacity}, that quantifies, through the concept of dynamical paths, the potential of an element of the system, and also, of the system itself, to propagate information. Among other examples, we study a heat diffusion model and SIR model to demonstrate the value of the proposed measure. We found, in the last case, that diffusion capacity can be used as a predictor of the evolution of the spreading process. In general, we show that the diffusion capacity provides an efficient tool to evaluate the performance of systems, and also, to identify and quantify structural modifications that could improve diffusion mechanisms.

physics.data-an↗

arXiv2020

Control of coherence resonance in multiplex neural networks

We study the dynamics of two neuronal populations weakly and mutually coupled in a multiplexed ring configuration. We simulate the neuronal activity with the stochastic FitzHugh-Nagumo (FHN) model. The two neuronal populations perceive different levels of noise: one population exhibits spiking activity induced by supra-threshold noise (layer 1), while the other population is silent in the absence of inter-layer coupling because its own level of noise is sub-threshold (layer 2). We find that, for appropriate levels of noise in layer 1, weak inter-layer coupling can induce coherence resonance (CR), anti-coherence resonance (ACR) and inverse stochastic resonance (ISR) in layer 2. We also find that a small number of randomly distributed inter-layer links are sufficient to induce these phenomena in layer 2. Our results hold for small and large neuronal populations.

nlin.AO↗

arXiv2020

Testing Critical Slowing Down as a Bifurcation Indicator in a Low-dissipation Dynamical System

We study a two-dimensional low-dissipation dynamical system with a control parameter that is swept linearly in time across a transcritical bifurcation. We investigate the relaxation time of a perturbation applied to a variable of the system and we show that critical slowing down may occur at a parameter value well above the bifurcation point. We test experimentally the occurrence of critical slowing down by applying a perturbation to the accessible control parameter and we find that this perturbation leaves the system behavior unaltered, thus providing no useful information on the occurrence of critical slowing down. The theoretical analysis reveals the reasons why these tests fail in predicting an incoming bifurcation.

nlin.PS↗

arXiv2020

Symbolic analysis of bursting dynamical regimes of Rulkov neural networks

Neurons modeled by the Rulkov map display a variety of dynamic regimes that include tonic spikes and chaotic bursting. Here we study an ensemble of bursting neurons coupled with the Watts-Strogatz small-world topology. We characterize the sequences of bursts using the symbolic method of time-series analysis known as ordinal analysis, which detects nonlinear temporal correlations. We show that the probabilities of the different symbols distinguish different dynamical regimes, which depend on the coupling strength and the network topology. These regimes have different spatio-temporal properties that can be visualized with raster plots.

q-bio.NC↗

arXiv2019

Extreme events in forced oscillatory media in 0, 1 and 2 dimensions

One of the open questions in the field of optical rogue waves is the relevance of the number of spatial dimensions in which waves propagate. Here we review recent results on extreme events obtained in 0, 1 and 2 spatial dimensions in the specific context of forced oscillatory media. We show that some dynamical scenarii can be relevant from 0 to 2D while others can take place only in sufficiently large number of spatial dimensions.

physics.optics↗

arXiv2018

Assessing diversity in multiplex networks

Diversity, understood as the variety of different elements or configurations that an extensive system has, is a crucial property that allows maintaining the system's functionality in a changing environment, where failures, random events or malicious attacks are often unavoidable. Despite the relevance of preserving diversity in the context of ecology, biology, transport, finances, etc., the elements or configurations that more contribute to the diversity are often unknown, and thus, they can not be protected against failures or environmental crises. This is due to the fact that there is no generic framework that allows identifying which elements or configurations have crucial roles in preserving the diversity of the system. Existing methods treat the level of heterogeneity of a system as a measure of its diversity, being unsuitable when systems are composed of a large number of elements with different attributes and types of interactions. Besides, with limited resources, one needs to find the best preservation policy, i.e., one needs to solve an optimization problem. Here we aim to bridge this gap by developing a metric between labeled graphs to compute the diversity of the system, which allows identifying the most relevant components, based on their contribution to a global diversity value. The proposed framework is suitable for large multiplex structures, which are constituted by a set of elements represented as nodes, which have different types of interactions, represented as layers. The proposed method allows us to find, in a genetic network (HIV-1), the elements with the highest diversity values, while in a European airline network, we systematically identify the companies that maximize (and those that less compromise) the variety of options for routes connecting different airports.

physics.soc-ph↗

arXiv2018

Differentiating resting brain states using ordinal symbolic analysis

Symbolic methods of analysis are valuable tools for investigating complex time-dependent signals. In particular, the ordinal method defines sequences of symbols according to the ordering in which values appear in a time series. This method has been shown to yield useful information, even when applied to signals with large noise contamination. Here we use ordinal analysis to investigate the transition between eyes closed (EC) and eyes open (EO) resting states. We analyze two {EEG} datasets (with 71 and 109 healthy subjects) with different recording conditions (sampling rates and the number of electrodes in the scalp). Using as diagnostic tools the permutation entropy, the entropy computed from symbolic transition probabilities, and an asymmetry coefficient (that measures the asymmetry of the likelihood of the transitions between symbols) we show that ordinal analysis applied to the raw data distinguishes the two brain states. In both datasets, we find that the EO state is characterized by higher entropies and lower asymmetry coefficient, as compared to the EC state. Our results thus show that these diagnostic tools have the potential for detecting and characterizing changes in time-evolving brain states.

physics.data-an↗

arXiv2017

Experimental characterization of the transition to coherence collapse in a semiconductor laser with optical feedback

Semiconductor lasers with time-delayed optical feedback display a wide range of dynamical regimes, which have found various practical applications. They also provide excellent testbeds for data analysis tools for characterizing complex signals. Recently, several of us have analyzed experimental intensity time-traces and quantitatively identified the onset of different dynamical regimes, as the laser's current increases. Specifically, we identified the onset of low-frequency fluctuations (LFFs), where the laser intensity displays abrupt dropouts, and the onset of coherence collapse (CC), where the intensity fluctuations are highly irregular. Here we map these regimes when both, the laser current and the feedback strength vary. We show that the shape of the distribution of intensity fluctuations (characterized by the standard deviation, the skewness, and the kurtosis) allows to distinguish between noise, LFFs, and CC, and to quantitatively determine (in spite of the gradual nature of the transitions) the boundaries of the three regimes. Ordinal analysis of the inter-dropout time intervals consistently identifies the three regimes occurring in the same parameter regions as the analysis of the intensity distribution. Simulations of the well-known time-delayed Lang-Kobayashi model are in good qualitative agreement with the observations.

physics.optics↗

arXiv2010

Crowd synchrony and quorum sensing in delay-coupled lasers

Crowd synchrony and quorum sensing arise when a large number of dynamical elements communicate with each other via a common information pool. Previous evidence in different fields, including chemistry, biology and civil engineering, has shown that this type of coupling leads to synchronization, when coupling is instantaneous and the number of coupled elements is large enough. Here we consider a situation in which the transmission of information between the system components and the coupling pool is not instantaneous. To that end, we model a system of semiconductor lasers optically coupled to a central laser with a delay. Our results show that, even though the lasers are non-identical due to their distinct optical frequencies, zero-lag synchronization arises. By changing a system parameter, we can switch between two different types of synchronization transition. The dependence of the transition with respect to the delay-coupling parameters is studied.

physics.optics↗

arXiv2008

Synchronizability of chaotic logistic maps in delayed complex networks

We study a network of coupled logistic maps whose interactions occur with a certain distribution of delay times. The local dynamics is chaotic in the absence of coupling and thus the network is a paradigm of a complex system. There are two regimes of synchronization, depending on the distribution of delays: when the delays are sufficiently heterogeneous the network synchronizes on a steady-state (that is unstable for the uncoupled maps); when the delays are homogeneous, it synchronizes in a time-dependent state (that is either periodic or chaotic). Using two global indicators we quantify the synchronizability on the two regimes, focusing on the roles of the network connectivity and the topology. The connectivity is measured in terms of the average number of links per node, and we consider various topologies (scale-free, small-world, star, and nearest-neighbor with and without a central hub). With weak connectivity and weak coupling strength, the network displays an irregular oscillatory dynamics that is largely independent of the topology and of the delay distribution. With heterogeneous delays, we find a threshold connectivity level below which the network does not synchronize, regardless of the network size. This minimum average number of neighbors seems to be independent of the delay distribution. We also analyze the effect of self-feedback loops and find that they have an impact on the synchronizability of small networks with large coupling strengths. The influence of feedback, enhancing or degrading synchronization, depends on the topology and on the distribution of delays.

nlin.CD↗

arXiv2003

Synchronization of globally coupled nonidentical maps with inhomogeneous delayed interactions

We study the synchronization of a coupled map lattice consisting of a one-dimensional chain of logistic maps. We consider global coupling with a time-delay that takes into account the finite velocity of propagation of interactions. We recently showed that clustering occurs for weak coupling, while for strong coupling the array synchronizes into a global state where each element sees all other elements in its current, present state [Physica A {\bf 325} (2003) 186, Phys. Rev. E {\bf 67} (2003) 056219]. In this paper we study the effects of in-homogeneities, both in the individual maps, which are non-identical maps evolving in period-2 orbits, and in the connection links, which have non-uniform strengths. We find that the global synchronization regime occurring for strong coupling is robust to heterogeneities: for strong enough average coupling the inhomogeneous array still synchronizes in a global state in which each element sees the other elements in positions close to its current state. However, the clustering behaviour occurring for small coupling is sensitive to inhomogeneities and differs from that occurring in the homogeneous array.

nlin.CD↗

arXiv2003

Delay-induced Synchronization Phenomena in an Array of Globally Coupled Logistic Maps

We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized states in which the elements of the array evolve along a periodic orbit of the uncoupled map, while the spatial correlation along the array is such that an individual map sees all other maps in his present, current, state. For values of the nonlinear parameter such that the uncoupled maps are chaotic, time-delayed mutual coupling suppress the chaotic behavior by stabilizing a periodic orbit which is unstable for the uncoupled maps. The stability analysis of the synchronized state allows us to calculate the range of the coupling strength in which global synchronization can be obtained.

nlin.CD↗

arXiv2002

Characterization of the anticipated synchronization regime in the coupled FitzHugh--Nagumo model for neurons

We characterize numerically the regime of anticipated synchronization in the coupled FitzHugh-Nagumo model for neurons. We consider two neurons, coupled unidirectionally (in a master-slave configuration), subject to the same random external forcing and with a recurrent inhibitory delayed connection in the slave neuron. We show that the scheme leads to anticipated synchronization, a regime in which the slave neuron fires the same train of pulses as the master neuron, but earlier in time. We characterize the synchronization in the parameter space (coupling strength, anticipation time) and introduce several quantities to measure the degree of synchronization.

cond-mat↗

arXiv2002

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.

cond-mat↗