259 research outputs found
Mechanisms of Zero-Lag Synchronization in Cortical Motifs
Zero-lag synchronization between distant cortical areas has been observed in
a diversity of experimental data sets and between many different regions of the
brain. Several computational mechanisms have been proposed to account for such
isochronous synchronization in the presence of long conduction delays: Of
these, the phenomenon of "dynamical relaying" - a mechanism that relies on a
specific network motif - has proven to be the most robust with respect to
parameter mismatch and system noise. Surprisingly, despite a contrary belief in
the community, the common driving motif is an unreliable means of establishing
zero-lag synchrony. Although dynamical relaying has been validated in empirical
and computational studies, the deeper dynamical mechanisms and comparison to
dynamics on other motifs is lacking. By systematically comparing
synchronization on a variety of small motifs, we establish that the presence of
a single reciprocally connected pair - a "resonance pair" - plays a crucial
role in disambiguating those motifs that foster zero-lag synchrony in the
presence of conduction delays (such as dynamical relaying) from those that do
not (such as the common driving triad). Remarkably, minor structural changes to
the common driving motif that incorporate a reciprocal pair recover robust
zero-lag synchrony. The findings are observed in computational models of
spiking neurons, populations of spiking neurons and neural mass models, and
arise whether the oscillatory systems are periodic, chaotic, noise-free or
driven by stochastic inputs. The influence of the resonance pair is also robust
to parameter mismatch and asymmetrical time delays amongst the elements of the
motif. We call this manner of facilitating zero-lag synchrony resonance-induced
synchronization, outline the conditions for its occurrence, and propose that it
may be a general mechanism to promote zero-lag synchrony in the brain.Comment: 41 pages, 12 figures, and 11 supplementary figure
Dynamics and Synchronization in Neuronal Models
La tesis está principalmente dedicada al modelado y simulación de sistemas neuronales. Entre otros aspectos se investiga el papel del ruido cuando actua sobre neuronas. El fenómeno de resonancia estocástica es caracterizado tanto a nivel teórico como reportado experimentalmente en un conjunto de neuronas del sistema motor. También se estudia el papel que juega la heterogeneidad en un conjunto de neuronas acopladas demostrando que la heterogeneidad en algunos parámetros de las neuronas puede mejorar la respuesta del sistema a una modulación periódica externa. También estudiamos del efecto de la topología y el retraso en las conexiones en una red neuronal. Se explora como las propiedades topológicas y los retrasos en la conducción de diferentes clases de redes afectan la capacidad de las neuronas para establecer una relación temporal bien definida mediante sus potenciales de acción. En particular, el concepto de consistencia se introduce y estudia en una red neuronal cuando plasticidad neuronal es tenida en cuenta entre las conexiones de la re
Emergence of Synchronous Oscillations in Neural Networks Excited by Noise
The presence of noise in non linear dynamical systems can play a constructive
role, increasing the degree of order and coherence or evoking improvements in
the performance of the system. An example of this positive influence in a
biological system is the impulse transmission in neurons and the
synchronization of a neural network. Integrating numerically the Fokker-Planck
equation we show a self-induced synchronized oscillation. Such an oscillatory
state appears in a neural network coupled with a feedback term, when this
system is excited by noise and the noise strength is within a certain range.Comment: 12 pages, 18 figure
An augmented moment method for stochastic ensembles with delayed couplings: I. Langevin model
By employing a semi-analytical dynamical mean-field approximation theory
previously proposed by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 041903
(2003)], we have developed an augmented moment method (AMM) in order to discuss
dynamics of an -unit ensemble described by linear and nonlinear Langevin
equations with delays. In AMM, original -dimensional {\it stochastic} delay
differential equations (SDDEs) are transformed to infinite-dimensional {\it
deterministic} DEs for means and correlations of local as well as global
variables. Infinite-order DEs arising from the non-Markovian property of SDDE,
are terminated at the finite level in the level- AMM (AMM), which
yields -dimensional deterministic DEs. Model calculations have been made
for linear and nonlinear Langevin models. The stationary solution of AMM for
the linear Langevin model with N=1 is nicely compared to the exact result. The
synchronization induced by an applied single spike is shown to be enhanced in
the nonlinear Langevin ensemble with model parameters locating at the
transition between oscillating and non-oscillating states. Results calculated
by AMM6 are in good agreement with those obtained by direct simulations.Comment: 18 pages, 3 figures, changed the title with re-arranged figures,
accepted in Phys. Rev. E with some change
An augmented moment method for stochastic ensembles with delayed couplings: II. FitzHugh-Nagumo model
Dynamics of FitzHugh-Nagumo (FN) neuron ensembles with time-delayed couplings
subject to white noises, has been studied by using both direct simulations and
a semi-analytical augmented moment method (AMM) which has been proposed in a
recent paper [H. Hasegawa, E-print: cond-mat/0311021]. For -unit FN neuron
ensembles, AMM transforms original -dimensional {\it stochastic} delay
differential equations (SDDEs) to infinite-dimensional {\it deterministic} DEs
for means and correlation functions of local and global variables.
Infinite-order recursive DEs are terminated at the finite level in the
level- AMM (AMM), yielding -dimensional deterministic DEs. When a
single spike is applied, the oscillation may be induced if parameters of
coupling strength, delay, noise intensity and/or ensemble size are appropriate.
Effects of these parameters on the emergence of the oscillation and on the
synchronization in FN neuron ensembles have been studied. The synchronization
shows the {\it fluctuation-induced} enhancement at the transition between
non-oscillating and oscillating states. Results calculated by AMM5 are in
fairly good agreement with those obtained by direct simulations.Comment: 15 pages, 3 figures; changed the title with correcting typos,
accepted in Phys. Rev. E with some change
Effect of the Topology and Delayed Interactions in Neuronal Networks Synchronization
As important as the intrinsic properties of an individual nervous cell stands the network of neurons in which it is embedded and by virtue of which it acquires great part of its responsiveness and functionality. In this study we have explored how the topological properties and conduction delays of several classes of neural networks affect the capacity of their constituent cells to establish well-defined temporal relations among firing of their action potentials. This ability of a population of neurons to produce and maintain a millisecond-precise coordinated firing (either evoked by external stimuli or internally generated) is central to neural codes exploiting precise spike timing for the representation and communication of information. Our results, based on extensive simulations of conductance-based type of neurons in an oscillatory regime, indicate that only certain topologies of networks allow for a coordinated firing at a local and long-range scale simultaneously. Besides network architecture, axonal conduction delays are also observed to be another important factor in the generation of coherent spiking. We report that such communication latencies not only set the phase difference between the oscillatory activity of remote neural populations but determine whether the interconnected cells can set in any coherent firing at all. In this context, we have also investigated how the balance between the network synchronizing effects and the dispersive drift caused by inhomogeneities in natural firing frequencies across neurons is resolved. Finally, we show that the observed roles of conduction delays and frequency dispersion are not particular to canonical networks but experimentally measured anatomical networks such as the macaque cortical network can display the same type of behavior
Spatiotemporal dynamics on small-world neuronal networks: The roles of two types of time-delayed coupling
We investigate temporal coherence and spatial synchronization on small-world
networks consisting of noisy Terman-Wang (TW) excitable neurons in dependence
on two types of time-delayed coupling: and
. For the former case, we show that time delay in
the coupling can dramatically enhance temporal coherence and spatial synchrony
of the noise-induced spike trains. In addition, if the delay time is
tuned to nearly match the intrinsic spike period of the neuronal network, the
system dynamics reaches a most ordered state, which is both periodic in time
and nearly synchronized in space, demonstrating an interesting resonance
phenomenon with delay. For the latter case, however, we can not achieve a
similar spatiotemporal ordered state, but the neuronal dynamics exhibits
interesting synchronization transition with time delay from zigzag fronts of
excitations to dynamic clustering anti-phase synchronization (APS), and further
to clustered chimera states which have spatially distributed anti-phase
coherence separated by incoherence. Furthermore, we also show how these
findings are influenced by the change of the noise intensity and the rewiring
probability. Finally, qualitative analysis is given to illustrate the numerical
results.Comment: 17 pages, 9 figure
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