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.
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 patte
rns, 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.
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 o
f 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.
