Isochronous dynamics in pulse coupled oscillator networks with delay

We consider a network of identical pulse-coupled oscillators with delay and all-to-all coupling. We demonstrate that the discontinuous nature of the dynamics induces the appearance of isochronous regions-subsets of the phase space filled with periodic orbits having the same period. For each fixed value of the network parameters, such an isochronous region corresponds to a subset of initial states on an appropriate surface of section with non-zero dimensions such that all periodic orbits in this set have qualitatively similar dynamical behaviour. We analytically and numerically study in detail such an isochronous region, give proof of its existence, and describe its properties. We further describe other isochronous regions that appear in the system.

Binding and segmentation via a neural mass model trained with Hebbian and anti-Hebbian mechanisms

Synchronization of neural activity in the gamma band, modulated by a slower theta rhythm, is assumed to play a significant role in binding and segmentation of multiple objects. In the present work, a recent neural mass model of a single cortical column is used to analyze the synaptic mechanisms which can warrant synchronization and desynchronization of cortical columns, during an autoassociation memory task. The model considers two distinct layers communicating via feedforward connections. The first layer receives the external input and works as an autoassociative network in the theta band, to recover a previously memorized object from incomplete information. The second realizes segmentation of different objects in the gamma band. To this end, units within both layers are connected with synapses trained on the basis of previous experience to store objects. The main model assumptions are: (i) recovery of incomplete objects is realized by excitatory synapses from pyramidal to pyramidal neurons in the same object; (ii) binding in the gamma range is realized by excitatory synapses from pyramidal neurons to fast inhibitory interneurons in the same object. These synapses (both at points i and ii) have a few ms dynamics and are trained with a Hebbian mechanism. (iii) Segmentation is realized with faster AMPA synapses, with rise times smaller than 1 ms, trained with an anti-Hebbian mechanism. Results show that the model, with the previous assumptions, can correctly reconstruct and segment three simultaneous objects, starting from incomplete knowledge. Segmentation of more objects is possible but requires an increased ratio between the theta and gamma periods.

RELATIONSHIP BETWEEN APPLICABILITY OF CURRENT-BASED SYNAPSES AND UNIFORMITY OF FIRING PATTERNS

The purpose of this paper is to identify situations in neural network modeling where current-based synapses are applicable. The applicability of current-based synapse model for studying post-transient behavior of neural networks is discussed in terms of average synaptic current strength induced by per spike during one firing cycle of a neuron (or briefly per spike synaptic current strength). It was found that current-based synapse models are applicable in both situations where both the interspike intervals of the neurons and the distribution of firing times of the neurons are uniform, and where the firing of all neurons is synchronized. If neither the interspike intervals nor the distribution of firing times of the neurons is uniform or the reversal potential is between the rest and threshold potentials, current-based synapse models may be oversimplified.

EXCITEMENT AND SYNCHRONIZATION OF SMALL-WORLD NEURONAL NETWORKS WITH SHORT-TERM SYNAPTIC PLASTICITY

Excitement and synchronization of electrically and chemically coupled Newman-Watts (NW) small-world neuronal networks with a short-term synaptic plasticity described by a modified Oja learning rule are investigated. For each type of neuronal network, the variation properties of synaptic weights are examined first. Then the effects of the learning rate, the coupling strength and the shortcut-adding probability on excitement and synchronization of the neuronal network are studied. It is shown that the synaptic learning suppresses the over-excitement, helps synchronization for the electrically coupled network but impairs synchronization for the chemically coupled one. Both the introduction of shortcuts and the increase of the coupling strength improve synchronization and they are helpful in increasing the excitement for the chemically coupled network, but have little effect on the excitement of the electrically coupled one.

TESTING OF INFORMATION CONDENSATION IN A MODEL REVERBERATING SPIKING NEURAL NETWORK

Information about external world is delivered to the brain in the form of structured in time spike trains. During further processing in higher areas, information is subjected to a certain condensation process, which results in formation of abstract conceptual images of external world, apparently, represented as certain uniform spiking activity partially independent on the input spike trains details. Possible physical mechanism of condensation at the level of individual neuron was discussed recently. In a reverberating spiking neural network, due to this mechanism the dynamics should settle down to the same uniform/ periodic activity in response to a set of various inputs. Since the same periodic activity may correspond to different input spike trains, we interpret this as possible candidate for information condensation mechanism in a network. Our purpose is to test this possibility in a network model consisting of five fully connected neurons, particularly, the influence of geometric size of the network, on its ability to condense information. Dynamics of 20 spiking neural networks of different geometric sizes are modelled by means of computer simulation. Each network was propelled into reverberating dynamics by applying various initial input spike trains. We run the dynamics until it becomes periodic. The Shannon's formula is used to calculate the amount of information in any input spike train and in any periodic state found. As a result, we obtain explicit estimate of the degree of information condensation in the networks, and conclude that it depends strongly on the net's geometric size.