How to enhance the dynamic range of excitatory-inhibitory excitable networks

Abstract

We investigate the collective dynamics of excitatory-inhibitory excitable networks in response to external stimuli. How to enhance the dynamic range, which represents the ability of networks to encode external stimuli, is crucial to many applications. We regard the system as a two-layer network (E layer and I layer) and explore the criticality and dynamic range on diverse networks. Interestingly, we find that phase transition occurs when the dominant eigenvalue of the E layer's weighted adjacency matrix is exactly 1, which is only determined by the topology of the E layer. Meanwhile, it is shown that the dynamic range is maximized at a critical state. Based on theoretical analysis, we propose an inhibitory factor for each excitatory node. We suggest that if nodes with high inhibitory factors are cut out from the I layer, the dynamic range could be further enhanced. However, because of the sparseness of networks and passive function of inhibitory nodes, the improvement is relatively small compared to the original dynamic range. Even so, this provides a strategy to enhance the dynamic range.

Feedback control stabilization of critical dynamics via resource transport on multilayer networks: How glia enable learning dynamics in the brain

“…Previous studies on purely excitatory networks [21] and networks having inhibitory nodes [17,22] show that λ determines the nature of the net- The maximum eigenvalue λ versus t, and (b) the total resource R versus t. The data plotted in black are 'baseline' results obtained using our model as described in the Model section of the paper. For the data plotted in red (labelled 'instability'), the initial evolution is the same as for the baseline data up until t = 100000 (marked in the figure by a vertical arrow), at which time the diffusion of resources between the glial cells is turned off, as described in the text.…”

Complementary action of chemical and electrical synapses to perception

“…Reference [17] shows theoretical analysis and simulations considering undirected connections. In this work, we have considered undirected electrical and directed chemical connections.…”

“…Pei and collaborators [17] investigated a excitatory-inhibitory excitable cellular automaton considering undirected random links. They verified that the dynamic range can be enhanced if the nodes with high inhibitory factors in the inhibitory layer are cut out.…”

“…Network consisting of excitatory and inhibitory neurons was considered to describe the primary visual cortex [16]. Pei and collaborators [17] investigated the behaviour of excitatory-inhibitory excitable networks with an external stimuli. They suggested that the dynamic range may be enhanced if high inhibitory factors are cut out from the inhibitory layer.…”

Criticality at Work: How Do Critical Networks Respond to Stimuli?

“…The ability to process stimulus intensities across several orders of magnitude is maximal at the point where stimuli are amplified as much as possible, but not so much as to engage the network in stable self-sustained activity. That result has been generalized in a number of models, including excitable networks with scale-free topology [6,7], with signal integration where discontinuous transitions are possible [39], or with an interplay between excitatory and inhibitory model neurons [40]. In fact, the mechanism does not even need to involve excitable waves, appearing also in a model of olfactory processing where a disinhibition transition involving inhibitory units takes place [41].…”