Modeling of spiking-bursting neural behavior using two-dimensional map

TLDR

The authors propose a simple two‑dimensional map model that replicates the spiking and spiking‑bursting dynamics of real biological neurons. The model comprises one fast and one slow variable, and phase‑portrait analysis explains spike and burst generation, map restructuring, and the dynamics of two coupled maps representing electrically coupled neurons, whose synchronization regimes vary with coupling strength. The model’s predictions agree with experimentally observed synchronization of chaotic spiking‑bursting behavior in real neurons.

Abstract

A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation of spikes, bursts of spikes, and restructuring of the map behavior are explained using phase portrait analysis. The dynamics of two coupled maps which model the behavior of two electrically coupled neurons is discussed. Synchronization regimes for spiking and bursting activity of these maps are studied as a function of coupling strength. It is demonstrated that the results of this model are in agreement with the synchronization of chaotic spiking-bursting behavior experimentally found in real biological neurons.