Wave-driven phase wave patterns in a ring of FitzHugh-Nagumo oscillators

TL;DR

This study models a cell-like system using FitzHugh-Nagumo oscillators to investigate how internal pacemaker-driven waves influence external phase wave patterns, revealing complex dynamical states and mechanisms.

Contribution

It introduces a biomimetic model combining internal and external FitzHugh-Nagumo systems to analyze wave interactions and phase patterning in a cell-like structure.

Findings

Identification of three distinct dynamical states based on coupling strength

Demonstration of phase wave propagation and interactions

A simplified linear model explains phase pattern mechanisms

Abstract

We explore a biomimetic model that simulates a cell, with the internal cytoplasm represented by a two-dimensional circular domain and the external cortex by a surrounding ring, both modeled using FitzHugh-Nagumo systems. The external ring is dynamically influenced by a pacemaker-driven wave originating from the internal domain, leading to the emergence of three distinct dynamical states based on the varying strengths of coupling. The range of dynamics observed includes phase patterning, the propagation of phase waves, and interactions between traveling and phase waves. A simplified linear model effectively explains the mechanisms behind the variety of phase patterns observed, providing insights into the complex interplay between a cell's internal and external environments.