# Hierarchical clusters in neuronal populations with plasticity

## TL;DR

This paper investigates frequency clustering in Hodgkin-Huxley neuron networks with spike timing-dependent plasticity, revealing how neural populations split into synchronized groups and how this may relate to slow oscillations in neural signals.

## Contribution

It introduces a phenomenological model for multi-clustering dynamics considering synaptic plasticity and identifies plasticity rules that lead to such clustering phenomena.

## Key findings

- Neural populations can split into multiple synchronized clusters.
- Amplitude of mean field exhibits low-frequency modulations.
- Plasticity rules can induce multi-clustering behavior.

## Abstract

We report the phenomenon of frequency clustering in a network of Hodgkin-Huxley neurons with spike timing-dependent plasticity. The clustering leads to a splitting of a neural population into a few groups synchronized at different frequencies. In this regime, the amplitude of the mean field undergoes low-frequency modulations, which may contribute to the mechanism of the emergence of slow oscillations of neural activity observed in spectral power of local field potentials or electroencephalographic signals at high frequencies. In addition to numerical simulations of such multi-clusters, we investigate the mechanisms of the observed phenomena using the simplest case of two clusters. In particular, we propose a phenomenological model which describes the dynamics of two clusters taking into account the adaptation of coupling weights. We also determine the set of plasticity functions (update rules), which lead to multi-clustering.