Pattern Formation in Excitable Neuronal Maps

TL;DR

This paper explores pattern formation in coupled excitable neuronal maps, revealing how different coupling types produce rings or spirals, and analyzing their evolution and persistence using a novel quantitative measure.

Contribution

It introduces a new method to quantify neuronal pattern dynamics and demonstrates how coupling strength influences pattern evolution in excitable maps.

Findings

Ring patterns expand with increased coupling

Spiral patterns evolve into turbulence at stronger coupling

Persistence decay varies with pattern type and coupling strength

Abstract

Coupled excitable systems can generate a variety of patterns. In this work, we investigate coupled Chialvo maps in two dimensions under two types of nearest-neighbor couplings. One coupling produces ringlike patterns, while the other produces spirals. The rings expand with increasing coupling, whereas spirals evolve into turbulence and dissipate at stronger coupling. To quantify these patterns, we introduce an analogue of the discriminant of the velocity gradient tensor and examine the persistence of its sign. For ring-type patterns, the persistence decays more slowly than exponentially, often following a power law or stretched exponential. When spiral structures remain intact, persistence saturates asymptotically and can exhibit superposed periodic oscillations, suggesting complex exponents at early times. These behaviors highlight deep connections with the underlying dynamics.