# How single neuron properties shape chaotic dynamics and signal transmission in random neural networks

## TL;DR

This paper develops a dynamical mean-field theory to understand how intrinsic neuron properties influence chaotic dynamics and signal transmission in large, randomly connected neural networks, revealing resonance phenomena and enhanced signal processing.

## Contribution

It introduces a novel theoretical framework linking single neuron dynamics to network chaos and signal transmission, applicable to realistic neural models.

## Key findings

- Power spectrum of chaotic activity emerges from nonlinear sharpening of single-unit responses.
- Networks with adaptation exhibit resonant chaos with narrow-band oscillations.
- Signal transmission is enhanced by adaptation in chaotic regimes.

## Abstract

While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the dynamical properties of nodes (such as single neurons) and recurrent connections interact to shape the effective dynamics in large randomly connected networks. A novel dynamical mean-field theory for strongly connected networks of multi-dimensional rate units shows that the power spectrum of the network activity in the chaotic phase emerges from a nonlinear sharpening of the frequency response function of single units. For the case of two-dimensional rate units with strong adaptation, we find that the network exhibits a state of "resonant chaos", characterized by robust, narrow-band stochastic oscillations. The coherence of stochastic oscillations is maximal at the onset of chaos and their correlation time scales with the adaptation timescale of single units. Surprisingly, the resonance frequency can be predicted from the properties of isolated units, even in the presence of heterogeneity in the adaptation parameters. In the presence of these internally-generated chaotic fluctuations, the transmission of weak, low-frequency signals is strongly enhanced by adaptation, whereas signal transmission is not influenced by adaptation in the non-chaotic regime. Our theoretical framework can be applied to other mechanisms at the level of single nodes, such as synaptic filtering, refractoriness or spike synchronization. These results advance our understanding of the interaction between the dynamics of single units and recurrent connectivity, which is a fundamental step toward the description of biologically realistic network models in the brain, or, more generally, networks of other physical or man-made complex dynamical units.