1,742 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
Statistical-Mechanical Measure of Stochastic Spiking Coherence in A Population of Inhibitory Subthreshold Neurons
By varying the noise intensity, we study stochastic spiking coherence (i.e.,
collective coherence between noise-induced neural spikings) in an inhibitory
population of subthreshold neurons (which cannot fire spontaneously without
noise). This stochastic spiking coherence may be well visualized in the raster
plot of neural spikes. For a coherent case, partially-occupied "stripes"
(composed of spikes and indicating collective coherence) are formed in the
raster plot. This partial occupation occurs due to "stochastic spike skipping"
which is well shown in the multi-peaked interspike interval histogram. The main
purpose of our work is to quantitatively measure the degree of stochastic
spiking coherence seen in the raster plot. We introduce a new spike-based
coherence measure by considering the occupation pattern and the pacing
pattern of spikes in the stripes. In particular, the pacing degree between
spikes is determined in a statistical-mechanical way by quantifying the average
contribution of (microscopic) individual spikes to the (macroscopic)
ensemble-averaged global potential. This "statistical-mechanical" measure
is in contrast to the conventional measures such as the "thermodynamic" order
parameter (which concerns the time-averaged fluctuations of the macroscopic
global potential), the "microscopic" correlation-based measure (based on the
cross-correlation between the microscopic individual potentials), and the
measures of precise spike timing (based on the peri-stimulus time histogram).
In terms of , we quantitatively characterize the stochastic spiking
coherence, and find that reflects the degree of collective spiking
coherence seen in the raster plot very well. Hence, the
"statistical-mechanical" spike-based measure may be used usefully to
quantify the degree of stochastic spiking coherence in a statistical-mechanical
way.Comment: 16 pages, 5 figures, to appear in the J. Comput. Neurosc
Beta-rhythm oscillations and synchronization transition in network models of Izhikevich neurons: effect of topology and synaptic type
Despite their significant functional roles, beta-band oscillations are least
understood. Synchronization in neuronal networks have attracted much attention
in recent years with the main focus on transition type. Whether one obtains
explosive transition or a continuous transition is an important feature of the
neuronal network which can depend on network structure as well as synaptic
types. In this study we consider the effect of synaptic interaction (electrical
and chemical) as well as structural connectivity on synchronization transition
in network models of Izhikevich neurons which spike regularly with beta
rhythms. We find a wide range of behavior including continuous transition,
explosive transition, as well as lack of global order. The stronger electrical
synapses are more conducive to synchronization and can even lead to explosive
synchronization. The key network element which determines the order of
transition is found to be the clustering coefficient and not the small world
effect, or the existence of hubs in a network. These results are in contrast to
previous results which use phase oscillator models such as the Kuramoto model.
Furthermore, we show that the patterns of synchronization changes when one goes
to the gamma band. We attribute such a change to the change in the refractory
period of Izhikevich neurons which changes significantly with frequency.Comment: 7 figures, 1 tabl
In-phase and anti-phase synchronization in noisy Hodgkin-Huxley neurons
We numerically investigate the influence of intrinsic channel noise on the
dynamical response of delay-coupling in neuronal systems. The stochastic
dynamics of the spiking is modeled within a stochastic modification of the
standard Hodgkin-Huxley model wherein the delay-coupling accounts for the
finite propagation time of an action potential along the neuronal axon. We
quantify this delay-coupling of the Pyragas-type in terms of the difference
between corresponding presynaptic and postsynaptic membrane potentials. For an
elementary neuronal network consisting of two coupled neurons we detect
characteristic stochastic synchronization patterns which exhibit multiple
phase-flip bifurcations: The phase-flip bifurcations occur in form of alternate
transitions from an in-phase spiking activity towards an anti-phase spiking
activity. Interestingly, these phase-flips remain robust in strong channel
noise and in turn cause a striking stabilization of the spiking frequency
A microscopic mechanism for self-organized quasi periodicity in random networks of non linear oscillators
Self-organized quasi periodicity is one of the most puzzling dynamical phases
observed in systems of non linear coupled oscillators. The single dynamical
units are not locked to the periodic mean field they produce, but they still
feature a coherent behavior, through an unexplained complex form of
correlation. We consider a class of leaky integrate-and-fire oscillators on
random sparse and massive networks with dynamical synapses, featuring
self-organized quasi periodicity, and we show how complex collective
oscillations arise from constructive interference of microscopic dynamics. In
particular, we find a simple quantitative relationship between two relevant
microscopic dynamical time scales and the macroscopic time scale of the global
signal. We show that the proposed relation is a general property of collective
oscillations, common to all the partially synchronous dynamical phases
analyzed. We argue that an analogous mechanism could be at the origin of
similar network dynamics.Comment: to appear in Phys. Rev.
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