Quantifying the Dynamical Complexity of Chaotic Time Series

Acknowledgements The author wishes to acknowledge G. Giacomelli, M. Mulansky, and L. Ricci for early discussions.Peer reviewedPublisher PD

Relaxation and coarsening of weakly-interacting breathers in a simplified DNLS chain

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On the equivalence of phase-oscillator and integrate-and-fire models

A quantitative comparison of various classes of oscillators (integrate-and-fire, Winfree, and Kuramoto-Daido type) is performed in the weak-coupling limit for a fully connected network of identical units. An almost perfect agreement is found, with only tiny differences among the models. We also show that the regime of self-consistent partial synchronization [SCPS] is rather general and can be observed for arbitrarily small coupling strength in any model class. As a by-product of our study, we are able to show that an integrate-and-fire model with a generic pulse shape can be always transformed into a similar model with $\delta$-pulses and a suitable phase response curve.Comment: 28 pages; 8 figures - accepted in PR

Self-sustained irregular activity in an ensemble of neural oscillators

An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is observed. The "synchronised phase", which emerges upon increasing the coupling strength, is characterized by highly-irregular fluctuations: a time-series analysis reveals that the dynamics of the order parameter is indeed high-dimensional. The complex dynamics appears to be the result of the non-perturbative action of a suitably shaped phase-response curve. Such mechanism differs from the often invoked balance between excitation and inhibition and might provide an alternative basis to account for the self-sustained brain activity in the resting state. The potential interest of this dynamical regime is further strengthened by its (microscopic) linear stability, which makes it quite suited for computational tasks. The overall study has been performed by combining analytical and numerical studies, starting from the linear stability analysis of the asynchronous regime, to include the Fourier analysis of the Kuramoto order parameter, the computation of various types of Lyapunov exponents, and a microscopic study of the inter-spike intervals.Comment: 11 pages, 10 figure

Noise-induced stabilization of collective dynamics

ACKNOWLEDGMENT This work has been financially supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 642563 (COSMOS).Peer reviewedPublisher PD

An open-system approach for the characterization of spatio-temporal chaos

We investigate the structure of the invariant measure of space-time chaos by adopting an "open-system" point of view. We consider large but finite windows of formally infinite one-dimensional lattices and quantify the effect of the interaction with the outer region by mapping the problem on the dynamical characterization of localized perturbations. This latter task is performed by suitably generalizing the concept of Lyapunov spectrum to cope with perturbations that propagate outside the region under investigation. As a result, we are able to introduce a "volume"-propagation velocity, i.e. the velocity with which ensembles of localized perturbations tend to fill volumes in the neighbouring regions.Comment: Submitted to J.Stat.Phys. - 26 pages, 7 eps-figures included. Keywords: High-dimensional Chaos; Fractals; Coupled map lattices; Numerical simulations of chaotic model

The one-dimensional Lennard-Jones system: collective fluctuations and breakdown of hydrodynamics

The dynamical correlations of a model consisting of particles constrained on the line and interacting with a nearest--neighbour Lennard--Jones potential are computed by molecular--dynamics simulations. A drastic qualitative change of the spectral shape, from a phonon--like to a diffusive form, is observed upon reducing the particle density even ad moderate temperatures. The latter scenario is due to the spontaneus fragmentation of the crystal--like structure into an ensemble of "clusters" colliding among themselves. In both cases, the spectral linewidths do not follow the usual q^2 behaviour for small wavenumbers q, thus signalling a breakdown of linearized hydrodynamics. This anomaly is traced back by the presence of correlations due to the reduced dimensionality.Comment: To be published in European Physical Journal