13,992 research outputs found
Effects of Noise in a Cortical Neural Model
Recently Segev et al. (Phys. Rev. E 64,2001, Phys.Rev.Let. 88, 2002) made
long-term observations of spontaneous activity of in-vitro cortical networks,
which differ from predictions of current models in many features. In this paper
we generalize the EI cortical model introduced in a previous paper (S.Scarpetta
et al. Neural Comput. 14, 2002), including intrinsic white noise and analyzing
effects of noise on the spontaneous activity of the nonlinear system, in order
to account for the experimental results of Segev et al.. Analytically we can
distinguish different regimes of activity, depending from the model parameters.
Using analytical results as a guide line, we perform simulations of the
nonlinear stochastic model in two different regimes, B and C. The Power
Spectrum Density (PSD) of the activity and the Inter-Event-Interval (IEI)
distributions are computed, and compared with experimental results. In regime B
the network shows stochastic resonance phenomena and noise induces aperiodic
collective synchronous oscillations that mimic experimental observations at 0.5
mM Ca concentration. In regime C the model shows spontaneous synchronous
periodic activity that mimic activity observed at 1 mM Ca concentration and the
PSD shows two peaks at the 1st and 2nd harmonics in agreement with experiments
at 1 mM Ca. Moreover (due to intrinsic noise and nonlinear activation function
effects) the PSD shows a broad band peak at low frequency. This feature,
observed experimentally, does not find explanation in the previous models.
Besides we identify parametric changes (namely increase of noise or decreasing
of excitatory connections) that reproduces the fading of periodicity found
experimentally at long times, and we identify a way to discriminate between
those two possible effects measuring experimentally the low frequency PSD.Comment: 25 pages, 10 figures, to appear in Phys. Rev.
Synchronization of coupled neural oscillators with heterogeneous delays
We investigate the effects of heterogeneous delays in the coupling of two
excitable neural systems. Depending upon the coupling strengths and the time
delays in the mutual and self-coupling, the compound system exhibits different
types of synchronized oscillations of variable period. We analyze this
synchronization based on the interplay of the different time delays and support
the numerical results by analytical findings. In addition, we elaborate on
bursting-like dynamics with two competing timescales on the basis of the
autocorrelation function.Comment: 18 pages, 14 figure
Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation
Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1 Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the possible consequences of chaotic dynamics for memory processing and learning
Finite Size Effects in Separable Recurrent Neural Networks
We perform a systematic analytical study of finite size effects in separable
recurrent neural network models with sequential dynamics, away from saturation.
We find two types of finite size effects: thermal fluctuations, and
disorder-induced `frozen' corrections to the mean-field laws. The finite size
effects are described by equations that correspond to a time-dependent
Ornstein-Uhlenbeck process. We show how the theory can be used to understand
and quantify various finite size phenomena in recurrent neural networks, with
and without detailed balance.Comment: 24 pages LaTex, with 4 postscript figures include
Does dynamics reflect topology in directed networks?
We present and analyze a topologically induced transition from ordered,
synchronized to disordered dynamics in directed networks of oscillators. The
analysis reveals where in the space of networks this transition occurs and its
underlying mechanisms. If disordered, the dynamics of the units is precisely
determined by the topology of the network and thus characteristic for it. We
develop a method to predict the disordered dynamics from topology. The results
suggest a new route towards understanding how the precise dynamics of the units
of a directed network may encode information about its topology.Comment: 7 pages, 4 figures, Europhysics Letters, accepte
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