Multistability, local pattern formation, and global collective firing in a small-world network of non-leaky integrate-and-fire neurons

TL;DR

This paper explores how a small-world network of non-leaky integrate-and-fire neurons exhibits multistability, local pattern formation, and global collective firing, depending on network parameters and initial conditions.

Contribution

It provides a numerical analysis of the diverse dynamical regimes, including local patterns and collective firing, in a biologically inspired neural network model.

Findings

Identification of local patterns like spiral and cyclic waves.

Observation of multistability depending on initial conditions.

Demonstration of interplay between local patterns and global firing.

Abstract

We investigate numerically the collective dynamical behavior of pulse-coupled non-leaky integrate-and-fire-neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for spontaneous firing for each neuron. We study network dynamics evolving from different sets of initial conditions in dependence on coupling strength and rewiring probability. Beside a homogeneous equilibrium state for low coupling strength, we observe different local patterns including cyclic waves, spiral waves, and turbulent-like patterns, which -- depending on network parameters -- interfere with the global collective firing of the neurons. We attribute the various network dynamics to distinct regimes in the parameter space. For the same network parameters different network dynamics can be observed depending on the set of initial conditions only. Such a multistable behavior and the interplay between local pattern formation and global collective firing may be attributable to the spatiotemporal dynamics of biological networks.