Final state sensitivity and fractal basin boundaries from coupled Chialvo neurons

TL;DR

This paper explores the complex basin structures and extreme sensitivity in coupled Chialvo neurons, revealing fractal boundaries and multistability that impact neural synchronization and neurological understanding.

Contribution

It provides a detailed analysis of basin geometry, chaos, and multistability in coupled neurons, highlighting the fractal nature of basin boundaries and their implications.

Findings

The coupled system exhibits multistability with two distinct attractors.

The basin boundary is fractal, causing extreme sensitivity to initial conditions.

Chaotic basin dominates the state space, affecting synchronization.

Abstract

We investigate and quantify the basin geometry and extreme final state uncertainty of two identical electrically asymmetrically coupled Chialvo neurons. The system's diverse behaviors are presented, along with the mathematical reasoning behind its chaotic and nonchaotic dynamics as determined by the structure of the coupled equations. The system is found to be multistable with two qualitatively different attractors. Although each neuron is individually nonchaotic, the chaotic basin takes up the vast majority of the coupled system's state space, but the nonchaotic basin stretches to infinity due to chance synchronization. The boundary between the basins is found to be fractal, leading to extreme final state sensitivity. This uncertainty and its potential effect on the synchronization of biological neurons may have significant implications for understanding human behavior and neurological disease.