arXiv subjects

S. R. Lopes

Publications and source records attributed to S. R. Lopes.

15 recordsLinked to original sources

arXiv2025

Classifying Complex Dynamical and Stochastic Systems via Physics-Based Recurrence Features

In this study, we employ the recently developed recurrence microstate probabilities as features to improve accuracy of several well-established machine learning (ML) algorithms. These algorithms are applied to classify discrete and continuous dynamical systems, as well as colored noise. We demonstrate that the dynamical characteristics quantified by this method are effectively captured in the recurrence microstate space, a space defined solely by the recurrence properties of the signal. This space change reduces dimensions, which also reduces the necessary time to perform calculations and obtain relevant information about the underlying system. Here, we also demonstrate that a few optimal machine learning (ML) algorithms are particularly effective for classification when combined with recurrence microstates. Furthermore, these new machine learning vectors significantly reduce memory usage and computational complexity, outperforming the direct analysis of raw data.

nlin.CD↗

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, $α$, that determines the strength of the correlation of the noise. To predict $α$ 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 $α$ 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 $α$ 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↗

arXiv2020

Synchronization malleability in neural networks under a distance-dependent coupling

We investigate the synchronization features of a network of spiking neurons under a distance-dependent coupling following a power-law model. The interplay between topology and coupling strength leads to the existence of different spatiotemporal patterns, corresponding to either non-synchronized or phase-synchronized states. Particularly interesting is what we call synchronization malleability, in which the system depicts significantly different phase synchronization degrees for the same parameters as a consequence of a different ordering of neural inputs. We analyze the functional connectivity of the network by calculating the mutual information between neuronal spike trains, allowing us to characterize the structures of synchronization in the network. We show that these structures are dependent on the ordering of the inputs for the parameter regions where the network presents synchronization malleability and we suggest that this is due to a complex interplay between coupling, connection architecture, and individual neural inputs.

q-bio.NC↗

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↗

arXiv2017

A novel entropy recurrence quantification analysis

The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on the concept of information entropy, in which the probabilities are associated to microstates defined from the recurrence phase space. Recurrence properties can properly be studied using recurrence plots, a methodology based on binary matrices where trajec- tories in phase space of dynamical systems are evaluated against other embedded trajectory. Our novel entropy methodology has several advantages compared to the traditional recurrence entropy defined in the literature, namely, the correct evaluation of the chaoticity level of the signal, the weak dependence on parameters, correct evaluation of periodic time series properties and more sensitivity to noise level of time series. Furthermore, the new entropy quantifier developed in this manuscript also fixes inconsistent results of the traditional recurrence entropy concept, reproducing classical results with novel insights.

stat.OT↗

arXiv2014

Super persistent transient in a master-slave configuration with Colpitts oscillators

Master-slave systems have been intensively investigated to model the application of chaos to communications. We considered Colpitts oscillators coupled according to a master-slave configuration to study chaos synchronisation. We revealed the existence of super persistent transients in this coupled system. Moreover, we showed that an additive noise added to the slave system may suppress chaos synchronisation. When synchronisation is not suppressed, the noise induces longer transients.

nlin.CD↗

arXiv2013

Model for tumour growth with treatment by continuous and pulsed chemotherapy

In this work we investigate a mathematical model describing tumour growth under a treatment by chemotherapy that incorporates time-delay related to the conversion from resting to hunting cells. We study the model using values for the parameters according to experimental results and vary some parameters relevant to the treatment of cancer. We find that our model exhibits a dynamical behaviour associated with the suppression of cancer cells, when either continuous or pulsed chemotherapy is applied according to clinical protocols, for a large range of relevant parameters. When the chemotherapy is successful, the predation coefficient of the chemotherapic agent acting on cancer cells varies with the infusion rate of chemotherapy according to an inverse relation. Finally, our model was able to reproduce the experimental results obtained by Michor and collaborators [Nature, 435, 1267 (2005)] about the exponential decline of cancer cells when patients are treated with the drug glivec.

q-bio.TO↗

arXiv2012

Effective transport barriers in nontwist systems

In fluids and plasmas with zonal flow reversed shear, a peculiar kind of transport barrier appears in the shearless region, one that is associated with a proper route of transition to chaos. Using a symplectic nontwist maps, which model such zonal flows, we investigate these barriers. In particular, the standard nontwist map, a paradigm of nontwist systems, is used to analyze the parameter dependence of the transport through a broken shearless barrier. Varying a proper control parameter, we identify the onset of structures with high stickiness that give rise to an effective barrier near the broken shearless curve. Several diagnostics are used: stickiness is measured by escape time and transmissivity plots, while barriers that separate different regions of stickiness are identified by employing two indicators in the phase space, the finite-time rotation number and the finite-time Lyapunov exponent.

nlin.CD↗

arXiv2011

Bursting synchronization in networks with long-range coupling mediated by a diffusing chemical substance

Many networks of physical and biological interest are characterized by a long-range coupling mediated by a chemical which diffuses through a medium in which oscillators are embedded. We considered a one-dimensional model for this effect for which the diffusion is fast enough so as to be implemented through a coupling whose intensity decays exponentially with the lattice distance. In particular, we analyzed the bursting synchronization of neurons described by two timescales (spiking and bursting activity), and coupled through such a long-range interaction network. One of the advantages of the model is that one can pass from a local (Laplacian) type of coupling to a global (all-to-all) one by varying a single parameter in the interaction term. We characterized bursting synchronization using an order parameter which undergoes a transition as the coupling parameters are changed through a critical value. We also investigated the role of an external time-periodic signal on the bursting synchronization properties of the network. We show potential applications in the control of pathological rhythms in biological neural networks.

nlin.CD↗

arXiv2011

Turing instability in oscillator chains with non-local coupling

We investigate analytically and numerically the conditions for the Turing instability to occur in a one-dimensional chain of nonlinear oscillators coupled non-locally in such a way that the coupling strength decreases with the spatial distance as a power-law. A range parameter makes possible to cover the two limiting cases of local (nearest-neighbor) and a global (all-to-all) couplings. We consider an example from a non-linear auto-catalytic reaction-diffusion model.

nlin.PS↗

arXiv2011

Finite-time rotation number: a fast indicator for chaotic dynamical structures

Lagrangian coherent structures are effective barriers, sticky regions, that separate phase space regions of different dynamical behavior. The usual way to detect such structures is via finite-time Lyapunov exponents. We show that similar results can be obtained for single-frequency systems from finite-time rotation numbers, which are much faster to compute. We illustrate our claim by considering examples of continuous and discrete-time dynamical systems of physical interest.

nlin.CD↗

arXiv2010

Global synchronization of bursting neurons in clustered networks

We investigate the collective dynamics of bursting neurons on clustered network. The clustered network is composed of subnetworks each presenting a small-world property, and in a given subnetwork each neuron has a probability to be connected to the other subnetworks. We give bounds for the critical coupling strength to obtain global burst synchronization in terms of the network structure, i.e., intracluster and intercluster probabilities connections. As the heterogeneity in the network is reduced the network global synchronization is improved. We show that the transitions to global synchrony may be abrupt or smooth depending on the intercluster probability.

nlin.CD↗

arXiv2003

Validity of numerical trajectories in the synchronization transition of complex systems

We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown {\it via} unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same non-hyperbolic properties.

nlin.CD↗

arXiv1999

Breakdown of Modulational Approximations in Nonlinear Wave Interaction

In this work we investigate the validity limits of the modulational approximation as a method to describe the nonlinear interaction of conservative wave fields. We focus on a nonlinear Klein-Gordon equation and suggest that the breakdown of the approximation is accompanied by a transition to regimes of spatiotemporal chaos.

chao-dyn↗

arXiv1998

Chaos and Energy Redistribution the Nonlinear Interaction of Two Spatio-Temporal Wave Triplets

In this paper we examine the spatio-temporal dynamics of two nonlinearly coupled wave triplets sharing two common modes. Our basic findings are the following. When spatial dependence is absent, the homogeneous manifold so obtained can be chaotic or regular. If chaotic, it drives energy diffusion from long to small wavelengths as soon as inhomogeneous perturbations are added to the system. If regular, one may yet have two distinct cases: (i) energy diffusion is again present if the inhomogeneous modes are linearly unstable and triplets are effectively coupled; (ii) energy diffusion is absent if the inhomogeneous modes are linearly stable or the triplets are uncoupled.

chao-dyn↗