191 research outputs found
Spike frequency adaptation affects the synchronization properties of networks of cortical oscillators
Oscillations in many regions of the cortex have common temporal characteristics with dominant frequencies centered around the 40 Hz (gamma) frequency range and the 5–10 Hz (theta) frequency range. Experimental results also reveal spatially synchronous oscillations, which are stimulus dependent (Gray&Singer, 1987;Gray, König, Engel, & Singer, 1989; Engel, König, Kreiter, Schillen, & Singer, 1992). This rhythmic activity suggests that the coherence of neural populations is a crucial feature of cortical dynamics (Gray, 1994). Using both simulations and a theoretical coupled oscillator approach, we demonstrate that the spike frequency adaptation seen in many pyramidal cells plays a subtle but important role in the dynamics of cortical networks. Without adaptation, excitatory connections among model pyramidal cells are desynchronizing. However, the slow processes associated with adaptation encourage stable synchronous behavior
Scalar Reduction of a Neural Field Model with Spike Frequency Adaptation
We study a deterministic version of a one- and two-dimensional attractor
neural network model of hippocampal activity first studied by Itskov et al
2011. We analyze the dynamics of the system on the ring and torus domain with
an even periodized weight matrix, assum- ing weak and slow spike frequency
adaptation and a weak stationary input current. On these domains, we find
transitions from spatially localized stationary solutions ("bumps") to
(periodically modulated) solutions ("sloshers"), as well as constant and
non-constant velocity traveling bumps depending on the relative strength of
external input current and adaptation. The weak and slow adaptation allows for
a reduction of the system from a distributed partial integro-differential
equation to a system of scalar Volterra integro-differential equations
describing the movement of the centroid of the bump solution. Using this
reduction, we show that on both domains, sloshing solutions arise through an
Andronov-Hopf bifurcation and derive a normal form for the Hopf bifurcation on
the ring. We also show existence and stability of constant velocity solutions
on both domains using Evans functions. In contrast to existing studies, we
assume a general weight matrix of Mexican-hat type in addition to a smooth
firing rate function.Comment: 60 pages, 22 figure
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
Formation of antiwaves in gap-junction-coupled chains of neurons
Using network models consisting of gap junction coupled Wang-Buszaki neurons,
we demonstrate that it is possible to obtain not only synchronous activity
between neurons but also a variety of constant phase shifts between 0 and \pi.
We call these phase shifts intermediate stable phaselocked states. These phase
shifts can produce a large variety of wave-like activity patterns in
one-dimensional chains and two-dimensional arrays of neurons, which can be
studied by reducing the system of equations to a phase model. The 2\pi periodic
coupling functions of these models are characterized by prominent higher order
terms in their Fourier expansion, which can be varied by changing model
parameters. We study how the relative contribution of the odd and even terms
affect what solutions are possible, the basin of attraction of those solutions
and their stability. These models may be applicable to the spinal central
pattern generators of the dogfish and also to the developing neocortex of the
neonatal rat
Phase Response Curves of Coupled Oscillators
Many real oscillators are coupled to other oscillators and the coupling can
affect the response of the oscillators to stimuli. We investigate phase
response curves (PRCs) of coupled oscillators. The PRCs for two weakly coupled
phase-locked oscillators are analytically obtained in terms of the PRC for
uncoupled oscillators and the coupling function of the system. Through
simulation and analytic methods, the PRCs for globally coupled oscillators are
also discussed.Comment: 5 pages 4 figur
Oscillations and chaos in the dynamics of the BCM learning rule
The BCM learning rule originally arose from experiments intended for measuring the selectivity of neurons in the primary visual cortex, and it dependence on input stimuli. This learning rule incorporates a dynamic LTP threshold, which depends on the time averaged postsynaptic activity. Although the BCM learning rule has been well studied and some experimental evidence of neuronal adherence has been found in the other areas of the brain, including the hippocampus, there is still much to be known about the dynamic behavior of this learning rule
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