Three-dimensional chimera patterns in networks of spiking neuron oscillators

TL;DR

This paper explores complex 3D chimera patterns in networks of spiking neuron oscillators modeled by LIF, revealing new structures and categorizing patterns based on coupling strength and phase velocity distributions.

Contribution

It introduces the first detailed analysis of 3D chimera states in neuron networks, including novel pattern types and quantitative categorization methods.

Findings

Identification of new 3D chimera structures like cylinders and cross-layered patterns.

Quantitative measures reveal two distinct families of patterns based on coupling strength.

Discontinuities in measures suggest critical transitions between pattern families.

Abstract

We study the stable spatiotemporal patterns that arise in a 3D network of neuron oscillators, whose dynamics is described by the Leaky Integrate-and-Fire (LIF) model. More specifically, we investigate the form of the chimera states induced by a 3D coupling matrix with nonlocal topology. The observed patterns are in many cases direct generalizations of the corresponding 2D patterns, e.~g. spheres, layers and cylinder grids. We also find cylindrical and "cross-layered" chimeras that do not have an equivalent in 2D systems. Quantitative measures are calculated, such as the ratio of synchronized and unsynchronized neurons as a function of the coupling range, the mean phase velocities and the distribution of neurons in mean phase velocities. Based on these measures the chimeras are categorized in two families. The first family of patterns is observed for weaker coupling and exhibits higher mean phase velocities for the unsynchronized areas of the network. The opposite holds for the second family where the unsynchronized areas have lower mean phase velocities. The various measures demonstrate discontinuities, indicating criticality as the parameters cross from the first family of patterns to the second.