Brain “rest” is defined -more or less unsuccessfully- as the state in which there is no explicit brain input or output. This work focuss on the question of whether such state can be comparable to any known dynamical state. For that purpose, correlation networks from human brain Functional Magnetic Resonance Imaging (fMRI) are constrasted with correlation networks extracted from numerical simulations of the Ising model in 2D, at different temperatures. For the critical temperature Tc, striking similarities appear in the most relevant statistical properties, making the two networks indistinguishable from each other. These results are interpreted here as lending support to the conjecture that the dynamics of the functioning brain is near a critical point.

Multistable dynamical systems have important applications as pattern recognition and memory storage devices. Conditions under which time-delayed recurrent loops of spiking neurons exhibit multistability are presented. Our results are illustrated on both a simple integrate-and-fire neuron and a Hodgkin-Huxley-type neuron, whose recurrent inputs are delayed versions of their output spike trains. Two kinds of multistability with respect to initial spiking functions are found, depending on whether the neuron is excitable or repetitively firing in the absence of feedback.

The dynamics of a recurrent inhibitory neural loop composed of a periodically spiking Aplysia motoneuron reciprocally connected to a computer are investigated as a function of the time delay, tau, for propagation around the loop. It is shown that for certain choices of tau, multiple qualitatively different neural spike trains co-exist. A mathematical model is constructed for the dynamics of this pulsed-coupled recurrent loop in which all parameters are readily measured experimentally: the phase resetting curve of the neuron for a given simulated postsynaptic current and tau. For choices of the parameters for which multiple spiking patterns co-exist in the experimental paradigm, the model exhibits multistability. Numerical simulations suggest that qualitatively similar results will occur if the motoneuron is replaced by several other types of neurons and that once tau becomes sufficiently long, multistability will be the dominant form of dynamical behavior. These observations suggest that great care must be taken in determining the etiology of qualitative changes in neural spiking patterns, particularly when propagation times around polysynaptic loops are long.

The multistability that arises in delayed feedback control mechanisms has applications for dynamic short term memory storage. Here we investigate the effects of multiplicative, Gaussian-distributed white noise on an integrate-and-fire model of a recurrent inhibitory neural loop: when the neuron fires an inhibitory pulse decreases the membrane potential by an amount ⌬ at time later. For appropriate choices of and ⌬, multistability occurs in the form of qualitatively different neuron firing patterns. In the absence of noise, the number and nature of the coexistent attractors can be precisely determined. When noise is added to ⌬, noise-induced transitions occur between the attractors. The mechanism for these transitions is characterized and it is shown that the rate of transitions has a nonexponential dependence on the noise variance. An electronic circuit is constructed to assess the impact of noise on memory storage.

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