http://www.gatsby.ucl.ac.uk/~beierh/neuro_jc/Sussillo_Abbott09_ChaoticNN.pdf

Generating coherent patterns of activity from chaotic neural networks.

Recurrent Network Models Of Sequence Generation And Memory

Here the author shows that an unstructured, sparsely connected network of model spiking neurons can display two different types of asynchronous activity: one in which an external input leads to a highly redundant response of different neurons that favors information transmission and another in which the firing rates of individual neurons fluctuate strongly in time and across neurons to provide a substrate for complex information processing.

Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons

Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, but they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a nonmonotonic function of stimulus frequency, revealing a "resonant" frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially. A prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate.

/pdf/stimulus-dependent-suppression-of-chaos-in-recurrent-neural-12ndqgtpgh.pdf

Stimulus-dependent suppression of chaos in recurrent neural networks

We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the time variations of their membrane potentials. They are coupled by synaptic connections acting on their resulting activity, a nonlinear function of their membrane potential. At the second (mesoscopic) scale, interacting populations of neurons are described individually by similar equations. The equations describing the dynamical and the stationary mean field behaviors are considered as functional equations on a set of stochastic processes. Using this new point of view allows us to prove that these equations are well-posed on any finite time interval and to provide, by a fixed point method, a constructive method for effectively computing their unique solution. This method is proved to converge to the unique solution and we characterize its complexity and convergence rate. We also provide partial results for the stationary problem on infinite time intervals. These results shed some new light on such neural mass models as the one of Jansen and Rit (Jansen and Rit 1995): their dynamics appears as a coarse approximation of the much richer dynamics that emerges from our analysis. Our numerical experiments confirm that the framework we propose and the numerical methods we derive from it provide a new and powerful tool for the exploration of neural behaviors at different scales.

/pdf/a-constructive-mean-field-analysis-of-multi-population-46geec1brn.pdf

A constructive mean field analysis of multi population neural networks with random synaptic weights and stochastic inputs

We study discrete parallel dynamics of a fully connected network of nonlinear elements interacting via long-range random asymmetric couplings under the influence of external noise. Using dynamical mean-field equations, which become exact in the thermodynamical limit, we calculate the activity and the maximal Lyapunov exponent of the network in dependence of a nonlinearity (gain) parameter and the noise intensity.

L. Molgedey

Papers

Suppressing chaos in neural networks by noise.