158 research outputs found
Chimera states in pulse coupled neural networks: the influence of dilution and noise
We analyse the possible dynamical states emerging for two symmetrically pulse
coupled populations of leaky integrate-and-fire neurons. In particular, we
observe broken symmetry states in this set-up: namely, breathing chimeras,
where one population is fully synchronized and the other is in a state of
partial synchronization (PS) as well as generalized chimera states, where both
populations are in PS, but with different levels of synchronization. Symmetric
macroscopic states are also present, ranging from quasi-periodic motions, to
collective chaos, from splay states to population anti-phase partial
synchronization. We then investigate the influence disorder, random link
removal or noise, on the dynamics of collective solutions in this model. As a
result, we observe that broken symmetry chimera-like states, with both
populations partially synchronized, persist up to 80 \% of broken links and up
to noise amplitudes 8 \% of threshold-reset distance. Furthermore, the
introduction of disorder on symmetric chaotic state has a constructive effect,
namely to induce the emergence of chimera-like states at intermediate dilution
or noise level.Comment: 15 pages, 7 figure, contribution for the Workshop "Nonlinear Dynamics
in Computational Neuroscience: from Physics and Biology to ICT" held in Turin
(Italy) in September 201
Linear and nonlinear information flow in spatially extended systems
Infinitesimal and finite amplitude error propagation in spatially extended
systems are numerically and theoretically investigated. The information
transport in these systems can be characterized in terms of the propagation
velocity of perturbations . A linear stability analysis is sufficient to
capture all the relevant aspects associated to propagation of infinitesimal
disturbances. In particular, this analysis gives the propagation velocity
of infinitesimal errors. If linear mechanisms prevail on the nonlinear ones
. On the contrary, if nonlinear effects are predominant finite
amplitude disturbances can eventually propagate faster than infinitesimal ones
(i.e. ). The finite size Lyapunov exponent can be successfully
employed to discriminate the linear or nonlinear origin of information flow. A
generalization of finite size Lyapunov exponent to a comoving reference frame
allows to state a marginal stability criterion able to provide both in
the linear and in the nonlinear case. Strong analogies are found between
information spreading and propagation of fronts connecting steady states in
reaction-diffusion systems. The analysis of the common characteristics of these
two phenomena leads to a better understanding of the role played by linear and
nonlinear mechanisms for the flow of information in spatially extended systems.Comment: 14 RevTeX pages with 13 eps figures, title/abstract changed minor
changes in the text accepted for publication on PR
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<alpha<2 and
it decreases from 1/4 to 1/5 for alpha>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.Comment: One figure and relative discussion changed. To be published in Eur.
Phys. J.
Sisyphus Effect in Pulse Coupled Excitatory Neural Networks with Spike-Timing Dependent Plasticity
The collective dynamics of excitatory pulse coupled neural networks with
spike timing dependent plasticity (STDP) is studied. Depending on the model
parameters stationary states characterized by High or Low Synchronization can
be observed. In particular, at the transition between these two regimes,
persistent irregular low frequency oscillations between strongly and weakly
synchronized states are observable, which can be identified as infraslow
oscillations with frequencies 0.02 - 0.03 Hz. Their emergence can be explained
in terms of the Sisyphus Effect, a mechanism caused by a continuous feedback
between the evolution of the coherent population activity and of the average
synaptic weight. Due to this effect, the synaptic weights have oscillating
equilibrium values, which prevents the neuronal population from relaxing into a
stationary macroscopic state.Comment: 18 pages, 24 figures, submitted to Physical Review
Analytical Estimation of the Maximal lyapunov Exponent in Oscillator Chains
An analytical expression for the maximal Lyapunov exponent in
generalized Fermi-Pasta-Ulam oscillator chains is obtained. The derivation is
based on the calculation of modulational instability growth rates for some
unstable periodic orbits. The result is compared with numerical simulations and
the agreement is good over a wide range of energy densities . At very
high energy density the power law scaling of with can be
also obtained by simple dimensional arguments, assuming that the system is
ruled by a single time scale. Finally, we argue that for repulsive and hard
core potentials in one dimension at large
.Comment: Latex, 10 pages, 5 Figs - Contribution to the Conference "Disorder
and Chaos" held in memory of Giovanni Paladin (Sept. 1997 - Rome) - submitted
to J. de Physiqu
Linear stability in networks of pulse-coupled neurons
In a first step towards the comprehension of neural activity, one should
focus on the stability of the various dynamical states. Even the
characterization of idealized regimes, such as a perfectly periodic spiking
activity, reveals unexpected difficulties. In this paper we discuss a general
approach to linear stability of pulse-coupled neural networks for generic
phase-response curves and post-synaptic response functions. In particular, we
present: (i) a mean-field approach developed under the hypothesis of an
infinite network and small synaptic conductances; (ii) a "microscopic" approach
which applies to finite but large networks. As a result, we find that no matter
how large is a neural network, its response to most of the perturbations
depends on the system size. There exists, however, also a second class of
perturbations, whose evolution typically covers an increasingly wide range of
time scales. The analysis of perfectly regular, asynchronous, states reveals
that their stability depends crucially on the smoothness of both the
phase-response curve and the transmitted post-synaptic pulse. The general
validity of this scenarion is confirmed by numerical simulations of systems
that are not amenable to a perturbative approach.Comment: 13 pages, 7 figures, submitted to Frontiers in Computational
Neuroscienc
Order Parameter for the Transition from Phase to Amplitude Turbulence
The maximal conserved phase gradient is introduced as an order parameter to
characterize the transition from phase- to defect-turbulence in the complex
Ginzburg-Landau equation. It has a finite value in the phase-turbulent regime
and decreases to zero when the transition to defect-turbulence is approached.
Solutions with a non-zero phase gradient are studied via a Lyapunov analysis.
The degree of "chaoticity" decreases for increasing values of the phase
gradient and finally leads to stable travelling wave solutions. A modified
Kuramoto-Sivashinsky equation for the phase-dynamics is able to reproduce the
main features of the stable waves and to explain their origin.Comment: 11 pages letter (PS file) and 3 figures (PS files
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