arXiv subjects

Alessandro Torcini

Publications and source records attributed to Alessandro Torcini.

At least 73 records · Page 4Linked to original sources

arXiv2007

Stability of the splay state in pulse--coupled networks

The stability of the dynamical states characterized by a uniform firing rate ({\it splay states}) is analyzed in a network of globally coupled leaky integrate-and-fire neurons. This is done by reducing the set of differential equations to a map that is investigated in the limit of large network size. We show that the stability of the splay state depends crucially on the ratio between the pulse--width and the inter-spike interval. More precisely, the spectrum of Floquet exponents turns out to consist of three components: (i) one that coincides with the predictions of the mean-field analysis [Abbott-van Vreesvijk, 1993]; (ii) a component measuring the instability of "finite-frequency" modes; (iii) a number of "isolated" eigenvalues that are connected to the characteristics of the single pulse and may give rise to strong instabilities (the Floquet exponent being proportional to the network size). Finally, as a side result, we find that the splay state can be stable even for inhibitory coupling.

cond-mat.dis-nn↗

arXiv2006

Double coherence resonance in neuron models driven by discrete correlated noise

We study the influence of correlations among discrete stochastic excitatory or inhibitory inputs on the response of the FitzHugh-Nagumo neuron model. For any level of correlation the emitted signal exhibits at some finite noise intensity a maximal degree of regularity, i.e., a coherence resonance. Furthermore, for either inhibitory or excitatory correlated stimuli a {\it Double Coherence Resonance} (DCR) is observable. DCR refers to a (absolute) maximum coherence in the output occurring for an optimal combination of noise variance and correlation. All these effects can be explained by taking advantage of the discrete nature of the correlated inputs.

cond-mat.dis-nn↗

arXiv2006

Synchronization of extended chaotic systems with long-range interactions: an analogy to Levy-flight spreading of epidemics

Spatially extended chaotic systems with power-law decaying interactions are considered. Two coupled replicas of such systems synchronize to a common spatio-temporal chaotic state above a certain coupling strength. The synchronization transition is studied as a nonequilibrium phase transition and its critical properties are analyzed at varying the interaction range. The transition is found to be always continuous, while the critical indexes vary with continuity with the power law exponent characterizing the interaction. Strong numerical evidences indicate that the transition belongs to the {\it anomalous directed percolation} family of universality classes found for L{é}vy-flight spreading of epidemic processes.

nlin.CD↗

arXiv2006

Coherent response of the Hodgkin-Huxley neuron in the high-input regime

We analyze the response of the Hodgkin-Huxley neuron to a large number of uncorrelated stochastic inhibitory and excitatory post-synaptic spike trains. In order to clarify the various mechanisms responsible for noise-induced spike triggering we examine the model in its silent regime. We report the coexistence of two distinct coherence resonances: the first one at low noise is due to the stimulation of "correlated" subthreshold oscillations; the second one at intermediate noise variances is instead related to the regularization of the emitted spike trains.

cond-mat.dis-nn↗

arXiv2006

Asymptotic and effective coarsening exponents in surface growth models

We consider a class of unstable surface growth models, z_t = -\partial_x J, developing a mound structure of size lambda and displaying a perpetual coarsening process, i.e. an endless increase in time of lambda. The coarsening exponents n, defined by the growth law of the mound size lambda with time, lambda=t^n, were previously found by numerical integration of the growth equations [A. Torcini and P. Politi, Eur. Phys. J. B 25, 519 (2002)]. Recent analytical work now allows to interpret such findings as finite time effective exponents. The asymptotic exponents are shown to appear at so large time that cannot be reached by direct integration of the growth equations. The reason for the appearance of effective exponents is clearly identified.

cond-mat.stat-mech↗

arXiv2006

Low frequency fluctuations in a Vertical Cavity Lasers: experiments versus Lang-Kobayashi dynamics

The limits of applicability of the Lang-Kobayashi (LK) model for a semiconductor laser with optical feedback are analyzed. The model equations, equipped with realistic values of the parameters, are investigated below solitary laser threshold where Low Frequency Fluctuations (LFF) are usually observed. The numerical findings are compared with experimental data obtained for the selected polarization mode from a Vertical Cavity Surface Laser (VCSEL) subject to polarization selective external feedback. The comparison reveals the bounds within which the dynamics of the LK can be considered as realistic. In particular, it clearly demonstrates that the deterministic LK, for realistic values of the linewidth enhancement factor $α$, reproduces the LFF only as a transient dynamics towards one of the stationary modes with maximal gain. A reasonable reproduction of real data from VCSEL can be obtained only by considering noisy LK or alternatively deterministic LK for extremely high $α$-values.

physics.optics↗

arXiv2006

Desynchronization in diluted neural networks

The dynamical behaviour of a weakly diluted fully-inhibitory network of pulse-coupled spiking neurons is investigated. Upon increasing the coupling strength, a transition from regular to stochastic-like regime is observed. In the weak-coupling phase, a periodic dynamics is rapidly approached, with all neurons firing with the same rate and mutually phase-locked. The strong-coupling phase is characterized by an irregular pattern, even though the maximum Lyapunov exponent is negative. The paradox is solved by drawing an analogy with the phenomenon of ``stable chaos'', i.e. by observing that the stochastic-like behaviour is "limited" to a an exponentially long (with the system size) transient. Remarkably, the transient dynamics turns out to be stationary.

cond-mat.dis-nn↗

arXiv2005

Dynamical response of the Hodgkin-Huxley model in the high-input regime

The response of the Hodgkin-Huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post-synaptic potentials is analyzed in detail. The model is examined in its three fundamental dynamical regimes: silence, bistability and repetitive firing. Its response is characterized in terms of statistical indicators (interspike-interval distributions and their first moments) as well as of dynamical indicators (autocorrelation functions and conditional entropies). In the silent regime, the coexistence of two different coherence resonances is revealed: one occurs at quite low noise and is related to the stimulation of subthreshold oscillations around the rest state; the second one (at intermediate noise variance) is associated with the regularization of the sequence of spikes emitted by the neuron. Bistability in the low noise limit can be interpreted in terms of jumping processes across barriers activated by stochastic fluctuations. In the repetitive firing regime a maximization of incoherence is observed at finite noise variance. Finally, the mechanisms responsible for spike triggering in the various regimes are clearly identified.

cond-mat.dis-nn↗

arXiv2005

Exploring the energy landscape of model proteins: a metric criterion for the determination of dynamical connectivity

A method to reconstruct the energy landscape of small peptides is presented with reference to a 2d off--lattice model. The starting point is a statistical analysis of the configurational distances between generic minima and directly connected pairs (DCP). As the mutual distance of DCP is typically much smaller than that of generic pairs, a metric criterion can be established to identify the great majority of DCP. Advantages and limits of this approach are thoroughly analyzed for three different heteropolymeric chains. A funnel--like structure of the energy landscape is found in all of the three cases, but the escape rates clearly reveal that the native configuration is more easily accessible (and is significantly more stable) for the sequence that is expected to behave as a real protein.

cond-mat.soft↗

arXiv2005

Nonlinearly driven transverse synchronization in coupled chaotic systems

Synchronization transitions are investigated in coupled chaotic maps. Depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur. When only two maps are considered we always find that the critical coupling $ε_l$ for chaotic synchronization can be predicted within a linear analysis by the vanishing of the transverse Lyapunov exponent $λ_T$. However, major differences between transitions driven by linear or nonlinear mechanisms are revealed by the dynamics of the transient toward the synchronized state. As a representative example of extended systems a one dimensional lattice of chaotic maps with power-law coupling is considered. In this high dimensional model finite amplitude instabilities may have a dramatic effect on the transition. For strong nonlinearities an exponential divergence of the synchronization times with the chain length can be observed above $ε_l$, notwithstanding the transverse dynamics is stable against infinitesimal perturbations at any instant. Therefore, the transition takes place at a coupling $ε_{nl}$ definitely larger than $ε_l$ and its origin is intrinsically nonlinear. The linearly driven transitions are continuous and can be described in terms of mean field results for non-equilibrium phase transitions with long range interactions. While the transitions dominated by nonlinear mechanisms appear to be discontinuous.

nlin.CD↗

arXiv2004

First-order microcanonical transitions in finite mean-field models

A microcanonical first order transition, connecting a clustered to a homogeneous phase, is studied from both the thermodynamic and dynamical point of view for a N-body Hamiltonian system with infinite-range couplings. In the microcanonical ensemble specific heat can be negative, but besides that, a microcanonical first order transition displays a temperature discontinuity as the energy is varied continuously (a dual phenomenon to the latent heat in the canonical ensemble). In the transition region, the entropy per particle exhibits, as a function of the order parameter, two relative maxima separated by a minimum. The relaxation of the metastable state is shown to be ruled by an activation process induced by intrinsic finite N fluctuations. In particular, numerical evidences are given that the escape time diverges exponentially with N, with a growth rate given by the entropy barrier.

cond-mat.stat-mech↗

arXiv2003

Thermally activated processes in polymer dynamics

Jumps between neighboring minima in the energy landscape of both homopolymeric and heteropolymeric chains are numerically investigated by determining the average escape time from different valleys. The numerical results are compared to the theoretical expression derived by Langer [J.S. Langer, Ann. Phys. 54 (1969) 258] with reference to a 2N-dimensional space. Our simulations indicate that the dynamics within the native valley is well described by a sequence of thermally activated process up to temperatures well above the folding temperature. At larger temperatures, systematic deviations from the Langer's estimate are instead observed. Several sources for such discrepancies are thoroughly discussed.

cond-mat.stat-mech↗

arXiv2003

Doppler Effect of Nonlinear Waves and Superspirals in Oscillatory Media

Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example, where waves originate from a source exhibiting a back-and-forth movement in radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves (``superspiral''). Using the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonous growth or decay as well as saturation of these modulations away from the source depending on the perturbation frequency. Our findings allow a consistent interpretation of recent experimental observations concerning superspirals and their decay to spatio-temporal chaos.

cond-mat.stat-mech↗

arXiv2002

The Hamiltonian Mean Field Model: from Dynamics to Statistical Mechanics and back

The thermodynamics and the dynamics of particle systems with infinite-range coupling display several unusual and new features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model represents a paradigmatic example of this class of systems. The present study addresses both attractive and repulsive interactions, with a particular emphasis on the description of clustering phenomena from a thermodynamical as well as from a dynamical point of view. The observed clustering transition can be first or second order, in the usual thermodynamical sense. In the former case, ensemble inequivalence naturally arises close to the transition, i.e. canonical and microcanonical ensembles give different results. In particular, in the microcanonical ensemble negative specific heat regimes and temperature jumps are observed. Moreover, having access to dynamics one can study non-equilibrium processes. Among them, the most striking is the emergence of coherent structures in the repulsive model, whose formation and dynamics can be studied either by using the tools of statistical mechanics or as a manifestation of the solutions of an associated Vlasov equation. The chaotic character of the HMF model has been also analyzed in terms of its Lyapunov spectrum.

cond-mat.stat-mech↗

arXiv2002

First and second order clustering transitions for a system with infinite-range attractive interaction

We consider a Hamiltonian system made of $N$ classical particles moving in two dimensions, coupled via an {\it infinite-range interaction} gauged by a parameter $A$. This system shows a low energy phase with most of the particles trapped in a unique cluster. At higher energy it exhibits a transition towards a homogenous phase. For sufficiently strong coupling $A$ an intermediate phase characterized by two clusters appears. Depending on the value of $A$ the observed transitions can be either second or first order in the canonical ensemble. In the latter case microcanonical results differ dramatically from canonical ones. However, a canonical analysis, extended to metastable and unstable states, is able to describe the microcanonical equilibrium phase. In particular, a microcanonical negative specific heat regime is observed in the proximity of the transition whenever it is canonically discontinuous. In this regime, {\it microcanonically stable} states are shown to correspond to {\it saddles} of the Helmholtz free energy, located inside the spinodal region.

cond-mat.stat-mech↗

arXiv2002

Coarsening process in one-dimensional surface growth models

Surface growth models may give rise to unstable growth with mound formation whose tipical linear size L increases in time. In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks. This picture applies to growth models for which the largest surface slope remains constant in time (model B): coarsening is known to be logarithmic in the absence of noise (L(t)=log t) and to follow a power law (L(t)=t^{1/3}) when noise is present. If surface slope increases indefinitely, the deterministic equation looks like a modified Cahn-Hilliard equation: here we study the late stage of coarsening through a linear stability analysis of the stationary periodic configurations and through a direct numerical integration. Analytical and numerical results agree with regard to the conclusion that steepening of mounds makes deterministic coarsening faster: if alpha is the exponent describing the steepening of the maximal slope M of mounds (M^alpha = L) we find that L(t)=t^n: n is equal to 1/4 for 1 2, according to n=alpha/(5*alpha -2). On the other side, the numerical solution of the corresponding stochastic equation clearly shows that in the presence of shot noise steepening of mounds makes coarsening slower than in model B: L(t)=t^{1/4}, irrespectively of alpha. Finally, the presence of a symmetry breaking term is shown not to modify the coarsening law of model alpha=1, both in the absence and in the presence of noise.

cond-mat.stat-mech↗

arXiv2001

Nonlinear Analysis of the Eckhaus Instability: Modulated Amplitude Waves and Phase Chaos with Non-zero Average Phase Gradient

We analyze the Eckhaus instability of plane waves in the one-dimensional complex Ginzburg-Landau equation (CGLE) and describe the nonlinear effects arising in the Eckhaus unstable regime. Modulated amplitude waves (MAWs) are quasi-periodic solutions of the CGLE that emerge near the Eckhaus instability of plane waves and cease to exist due to saddle-node bifurcations (SN). These MAWs can be characterized by their average phase gradient $ν$ and by the spatial period P of the periodic amplitude modulation. A numerical bifurcation analysis reveals the existence and stability properties of MAWs with arbitrary $ν$ and P. MAWs are found to be stable for large enough $ν$ and intermediate values of P. For different parameter values they are unstable to splitting and attractive interaction between subsequent extrema of the amplitude. Defects form from perturbed plane waves for parameter values above the SN of the corresponding MAWs. The break-down of phase chaos with average phase gradient $ν$ > 0 (``wound-up phase chaos'') is thus related to these SNs. A lower bound for the break-down of wound-up phase chaos is given by the necessary presence of SNs and an upper bound by the absence of the splitting instability of MAWs.

nlin.CD↗

arXiv2001

Front Propagation in Chaotic and Noisy Reaction-Diffusion Systems: a Discrete-Time Map Approach

We study the front propagation in Reaction-Diffusion systems whose reaction dynamics exhibits an unstable fixed point and chaotic or noisy behaviour. We have examined the influence of chaos and noise on the front propagation speed and on the wandering of the front around its average position. Assuming that the reaction term acts periodically in an impulsive way, the dynamical evolution of the system can be written as the convolution between a spatial propagator and a discrete-time map acting locally. This approach allows us to perform accurate numerical analysis. They reveal that in the pulled regime the front speed is basically determined by the shape of the map around the unstable fixed point, while its chaotic or noisy features play a marginal role. In contrast, in the pushed regime the presence of chaos or noise is more relevant. In particular the front speed decreases when the degree of chaoticity is increased, but it is not straightforward to derive a direct connection between the chaotic properties (e.g. the Lyapunov exponent) and the behaviour of the front. As for the fluctuations of the front position, we observe for the noisy maps that the associated mean square displacement grows in time as $t^{1/2}$ in the pushed case and as $t^{1/4}$ in the pulled one, in agreement with recent findings obtained for continuous models with multiplicative noise. Moreover we show that the same quantity saturates when a chaotic deterministic dynamics is considered for both pushed and pulled regimes.

cond-mat.stat-mech↗