Chimera patterns in two-dimensional networks of coupled neurons

TL;DR

This paper explores diverse two-dimensional chimera patterns in coupled neuron models, revealing multistability and pattern transitions influenced by parameters, with many patterns following similar scaling rules across models.

Contribution

It provides the first detailed analysis of 2D chimera patterns in coupled FitzHugh-Nagumo and Leaky Integrate-and-Fire neuron networks, highlighting multistability and pattern scaling laws.

Findings

Multiple 2D chimera patterns including spots, rings, stripes, and grids.

Presence of multistability with different initial conditions leading to different patterns.

Pattern characteristics such as ring diameter scale linearly with coupling radius.

Abstract

We discuss synchronization patterns in networks of FitzHugh-Nagumo and Leaky Integrate-and-Fire oscillators coupled in a two-dimensional toroidal geometry. Common feature between the two models is the presence of fast and slow dynamics, a typical characteristic of neurons. Earlier studies have demonstrated that both models when coupled nonlocally in one-dimensional ring networks produce chimera states for a large range of parameter values. In this study, we give evidence of a plethora of two-dimensional chimera patterns of various shapes including spots, rings, stripes, and grids, observed in both models, as well as additional patterns found mainly in the FitzHugh-Nagumo system. Both systems exhibit multistability: For the same parameter values, different initial conditions give rise to different dynamical states. Transitions occur between various patterns when the parameters (coupling range, coupling strength, refractory period, and coupling phase) are varied. Many patterns observe in the two models follow similar rules. For example the diameter of the rings grows linearly with the coupling radius.