251 research outputs found
Topological Speed Limits to Network Synchronization
We study collective synchronization of pulse-coupled oscillators interacting
on asymmetric random networks. We demonstrate that random matrix theory can be
used to accurately predict the speed of synchronization in such networks in
dependence on the dynamical and network parameters. Furthermore, we show that
the speed of synchronization is limited by the network connectivity and stays
finite, even if the coupling strength becomes infinite. In addition, our
results indicate that synchrony is robust under structural perturbations of the
network dynamics.Comment: 5 pages, 3 figure
Sporadicity and synchronization in one-dimensional asymmetrically coupled maps
A one-dimensional chain of sporadic maps with asymmetric nearest neighbour
couplings is numerically studied. It is shown that in the region of strong
asymmetry the system becomes spatially fully synchronized, even in the
thermodinamic limit, while the Lyapunov exponent is zero. For weak asymmetry
the synchronization is no more complete, and the Lyapunov exponent becomes
positive. In addition one has a clear relation between temporal and spatial
chaos, {\it i.e.}: a positive effective Lyapunov exponent corresponds to a lack
of synchronization and {\it vice versa}Comment: 9 pages + 3 figures (postscript appended uuencoded tar), IOP style
(appended uuencoded compress
A statistical mechanics of an oscillator associative memory with scattered natural frequencies
Analytic treatment of a non-equilibrium random system with large degrees of
freedoms is one of most important problems of physics. However, little research
has been done on this problem as far as we know. In this paper, we propose a
new mean field theory that can treat a general class of a non-equilibrium
random system. We apply the present theory to an analysis for an associative
memory with oscillatory elements, which is a well-known typical random system
with large degrees of freedoms.Comment: 8 pages, 4 figure
Noise Induced Coherence in Neural Networks
We investigate numerically the dynamics of large networks of globally
pulse-coupled integrate and fire neurons in a noise-induced synchronized state.
The powerspectrum of an individual element within the network is shown to
exhibit in the thermodynamic limit () a broadband peak and an
additional delta-function peak that is absent from the powerspectrum of an
isolated element. The powerspectrum of the mean output signal only exhibits the
delta-function peak. These results are explained analytically in an exactly
soluble oscillator model with global phase coupling.Comment: 4 pages ReVTeX and 3 postscript figure
Acceleration effect of coupled oscillator systems
We have developed a curved isochron clock (CIC) by modifying the radial
isochron clock to provide a clean example of the acceleration (deceleration)
effect. By analyzing a two-body system of coupled CICs, we determined that an
unbalanced mutual interaction caused by curved isochron sets is the minimum
mechanism needed for generating the acceleration (deceleration) effect in
coupled oscillator systems. From this we can see that the Sakaguchi and
Kuramoto (SK) model which is a class of non-frustrated mean feild model has an
acceleration (deceleration) effect mechanism. To study frustrated coupled
oscillator systems, we extended the SK model to two oscillator associative
memory models, one with symmetric and one with asymmetric dilution of coupling,
which also have the minimum mechanism of the acceleration (deceleration)
effect. We theoretically found that the {\it Onsager reaction term} (ORT),
which is unique to frustrated systems, plays an important role in the
acceleration (de! celeration) effect. These two models are ideal for evaluating
the effect of the ORT because, with the exception of the ORT, they have the
same order parameter equations. We found that the two models have identical
macroscopic properties, except for the acceleration effect caused by the ORT.
By comparing the results of the two models, we can extract the effect of the
ORT from only the rotation speeds of the oscillators.Comment: 35 pages, 10 figure
Linear stability analysis of retrieval state in associative memory neural networks of spiking neurons
We study associative memory neural networks of the Hodgkin-Huxley type of
spiking neurons in which multiple periodic spatio-temporal patterns of spike
timing are memorized as limit-cycle-type attractors. In encoding the
spatio-temporal patterns, we assume the spike-timing-dependent synaptic
plasticity with the asymmetric time window. Analysis for periodic solution of
retrieval state reveals that if the area of the negative part of the time
window is equivalent to the positive part, then crosstalk among encoded
patterns vanishes. Phase transition due to the loss of the stability of
periodic solution is observed when we assume fast alpha-function for direct
interaction among neurons. In order to evaluate the critical point of this
phase transition, we employ Floquet theory in which the stability problem of
the infinite number of spiking neurons interacting with alpha-function is
reduced into the eigenvalue problem with the finite size of matrix. Numerical
integration of the single-body dynamics yields the explicit value of the
matrix, which enables us to determine the critical point of the phase
transition with a high degree of precision.Comment: Accepted for publication in Phys. Rev.
Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises
Dynamics of an ensemble of -unit FitzHugh-Nagumo (FN) neurons subject to
white noises has been studied by using a semi-analytical dynamical mean-field
(DMF) theory in which the original -dimensional {\it stochastic}
differential equations are replaced by 8-dimensional {\it deterministic}
differential equations expressed in terms of moments of local and global
variables. Our DMF theory, which assumes weak noises and the Gaussian
distribution of state variables, goes beyond weak couplings among constituent
neurons. By using the expression for the firing probability due to an applied
single spike, we have discussed effects of noises, synaptic couplings and the
size of the ensemble on the spike timing precision, which is shown to be
improved by increasing the size of the neuron ensemble, even when there are no
couplings among neurons. When the coupling is introduced, neurons in ensembles
respond to an input spike with a partial synchronization. DMF theory is
extended to a large cluster which can be divided into multiple sub-clusters
according to their functions. A model calculation has shown that when the noise
intensity is moderate, the spike propagation with a fairly precise timing is
possible among noisy sub-clusters with feed-forward couplings, as in the
synfire chain. Results calculated by our DMF theory are nicely compared to
those obtained by direct simulations. A comparison of DMF theory with the
conventional moment method is also discussed.Comment: 29 pages, 2 figures; augmented the text and added Appendice
Spike-Train Responses of a Pair of Hodgkin-Huxley Neurons with Time-Delayed Couplings
Model calculations have been performed on the spike-train response of a pair
of Hodgkin-Huxley (HH) neurons coupled by recurrent excitatory-excitatory
couplings with time delay. The coupled, excitable HH neurons are assumed to
receive the two kinds of spike-train inputs: the transient input consisting of
impulses for the finite duration (: integer) and the sequential input
with the constant interspike interval (ISI). The distribution of the output ISI
shows a rich of variety depending on the coupling strength and the
time delay. The comparison is made between the dependence of the output ISI for
the transient inputs and that for the sequential inputs.Comment: 19 pages, 4 figure
Chaos in neural networks with a nonmonotonic transfer function
Time evolution of diluted neural networks with a nonmonotonic transfer
function is analitically described by flow equations for macroscopic variables.
The macroscopic dynamics shows a rich variety of behaviours: fixed-point,
periodicity and chaos. We examine in detail the structure of the strange
attractor and in particular we study the main features of the stable and
unstable manifolds, the hyperbolicity of the attractor and the existence of
homoclinic intersections. We also discuss the problem of the robustness of the
chaos and we prove that in the present model chaotic behaviour is fragile
(chaotic regions are densely intercalated with periodicity windows), according
to a recently discussed conjecture. Finally we perform an analysis of the
microscopic behaviour and in particular we examine the occurrence of damage
spreading by studying the time evolution of two almost identical initial
configurations. We show that for any choice of the parameters the two initial
states remain microscopically distinct.Comment: 12 pages, 11 figures. Accepted for publication in Physical Review E.
Originally submitted to the neuro-sys archive which was never publicly
announced (was 9905001
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