Dynamical manifold dimensionality as characterization measure of chimera states in bursting neuronal networks

TL;DR

This paper introduces the correlation dimension as a new method to identify and characterize chimera states in bursting neuronal networks, improving detection over existing techniques.

Contribution

The study presents the correlation dimension as a novel, effective measure for detecting chimera states in bursting neurons, applicable to both simulated and experimental data.

Findings

Correlation dimension effectively detects chimeras in burst neurons.

The method distinguishes between spike and burst incoherence.

Applicable to various dynamic systems beyond neural networks.

Abstract

Methods that distinguish dynamical regimes in networks of active elements make it possible to design the dynamics of models of realistic networks. A particularly salient example is partial synchronization, which may play a pivotal role in elucidating the dynamics of biological neural networks. Such emergent partial synchronization in structurally homogeneous networks is commonly denoted as chimera states. While several methods for detecting chimeras in networks of spiking neurons have been proposed, these are less effective when applied to networks of bursting neurons. Here we introduce the correlation dimension as a novel approach to identifying dynamic network states. To assess the viability of this new method, we study a network of intrinsically Hindmarsh-Rose neurons with non-local connections. In comparison to other measures of chimera states, the correlation dimension effectively characterizes chimeras in burst neurons, whether the incoherence arises in spikes or bursts. The generality of dimensionality measures inherent in the correlation dimension renders this approach applicable to any dynamic system, facilitating the comparison of simulated and experimental data. We anticipate that this methodology will enable the tuning and simulation of when modelling intricate network processes, contributing to a deeper understanding of neural dynamics.