3,711 research outputs found
Noise-induced synchronization and anti-resonance in excitable systems; Implications for information processing in Parkinson's Disease and Deep Brain Stimulation
We study the statistical physics of a surprising phenomenon arising in large
networks of excitable elements in response to noise: while at low noise,
solutions remain in the vicinity of the resting state and large-noise solutions
show asynchronous activity, the network displays orderly, perfectly
synchronized periodic responses at intermediate level of noise. We show that
this phenomenon is fundamentally stochastic and collective in nature. Indeed,
for noise and coupling within specific ranges, an asymmetry in the transition
rates between a resting and an excited regime progressively builds up, leading
to an increase in the fraction of excited neurons eventually triggering a chain
reaction associated with a macroscopic synchronized excursion and a collective
return to rest where this process starts afresh, thus yielding the observed
periodic synchronized oscillations. We further uncover a novel anti-resonance
phenomenon: noise-induced synchronized oscillations disappear when the system
is driven by periodic stimulation with frequency within a specific range. In
that anti-resonance regime, the system is optimal for measures of information
capacity. This observation provides a new hypothesis accounting for the
efficiency of Deep Brain Stimulation therapies in Parkinson's disease, a
neurodegenerative disease characterized by an increased synchronization of
brain motor circuits. We further discuss the universality of these phenomena in
the class of stochastic networks of excitable elements with confining coupling,
and illustrate this universality by analyzing various classical models of
neuronal networks. Altogether, these results uncover some universal mechanisms
supporting a regularizing impact of noise in excitable systems, reveal a novel
anti-resonance phenomenon in these systems, and propose a new hypothesis for
the efficiency of high-frequency stimulation in Parkinson's disease
Noise-induced escape in an excitable system
We consider the stochastic dynamics of escape in an excitable system, the FitzHugh-Nagumo (FHN) neuronal model, for different classes of excitability. We discuss, first, the threshold structure of the FHN model as an example of a system without a saddle state. We then develop a nonlinear (nonlocal) stability approach based on the theory of large fluctuations, including a finite-noise correction, to describe noise-induced escape in the excitable regime. We show that the threshold structure is revealed via patterns of most probable (optimal) fluctuational paths. The approach allows us to estimate the escape rate and the exit location distribution. We compare the responses of a monostable resonator and monostable integrator to stochastic input signals and to a mixture of periodic and stochastic stimuli. Unlike the commonly used local analysis of the stable state, our nonlocal approach based on optimal paths yields results that are in good agreement with direct numerical simulations of the Langevin equation
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.Comment: 5 pages - 5 eps figures, contribution presented to the conference CNS
2006 held in Edinburgh (UK), to appear on Neurocomputin
Noise-induced memory in extended excitable systems
We describe a form of memory exhibited by extended excitable systems driven
by stochastic fluctuations. Under such conditions, the system self-organizes
into a state characterized by power-law correlations thus retaining long-term
memory of previous states. The exponents are robust and model-independent. We
discuss novel implications of these results for the functioning of cortical
neurons as well as for networks of neurons.Comment: 4 pages, latex + 5 eps figure
Noise-induced inhibitory suppression of malfunction neural oscillators
Motivated by the aim to find new medical strategies to suppress undesirable
neural synchronization we study the control of oscillations in a system of
inhibitory coupled noisy oscillators. Using dynamical properties of inhibition,
we find regimes when the malfunction oscillations can be suppressed but the
information signal of a certain frequency can be transmitted through the
system. The mechanism of this phenomenon is a resonant interplay of noise and
the transmission signal provided by certain value of inhibitory coupling.
Analyzing a system of three or four oscillators representing neural clusters,
we show that this suppression can be effectively controlled by coupling and
noise amplitudes.Comment: 10 pages, 14 figure
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
Time-delayed feedback in neurosystems
The influence of time delay in systems of two coupled excitable neurons is
studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in
the coupling between neurons or in a self-feedback loop. The stochastic
synchronization of instantaneously coupled neurons under the influence of white
noise can be deliberately controlled by local time-delayed feedback. By
appropriate choice of the delay time synchronization can be either enhanced or
suppressed. In delay-coupled neurons, antiphase oscillations can be induced for
sufficiently large delay and coupling strength. The additional application of
time-delayed self-feedback leads to complex scenarios of synchronized in-phase
or antiphase oscillations, bursting patterns, or amplitude death.Comment: 13 pages, 13 figure
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