Symbolic analysis of bursting dynamical regimes of Rulkov neural networks

TL;DR

This paper analyzes the complex bursting behaviors of Rulkov neural networks using symbolic ordinal analysis, revealing how coupling strength and network topology influence different dynamical regimes and their spatio-temporal properties.

Contribution

It introduces a symbolic ordinal analysis approach to characterize neural bursting regimes in coupled Rulkov networks, linking dynamics to network topology and coupling.

Findings

Different dynamical regimes are distinguishable by symbol probabilities.

Coupling strength affects the transition between regimes.

Network topology influences spatio-temporal bursting patterns.

Abstract

Neurons modeled by the Rulkov map display a variety of dynamic regimes that include tonic spikes and chaotic bursting. Here we study an ensemble of bursting neurons coupled with the Watts-Strogatz small-world topology. We characterize the sequences of bursts using the symbolic method of time-series analysis known as ordinal analysis, which detects nonlinear temporal correlations. We show that the probabilities of the different symbols distinguish different dynamical regimes, which depend on the coupling strength and the network topology. These regimes have different spatio-temporal properties that can be visualized with raster plots.