Transformation between dense and sparse spirals in symmetrical bistable media

TL;DR

This paper investigates how dense spirals in a bistable FitzHugh-Nagumo model can transform into two types of sparse spirals through bifurcation, influenced by boundary effects, leading to novel spiral behaviors.

Contribution

It reveals the transformation mechanisms between dense and sparse spirals and highlights the significant role of boundary effects in spiral dynamics.

Findings

Dense spirals transform into PPSS and NPSS via subcritical bifurcation.

Boundary effects influence the type of sparse spiral formed.

Novel outward-petaled spiral meandering observed due to boundary influence.

Abstract

Transformation between dense and sparse spirals is studied numerically based on a bistable FitzHugh-Nagumo model. It is found that the dense spiral can transform into two types of sparse spirals via a subcritical bifurcation: Positive Phase Sparse Spiral (PPSS) and Negative Phase Sparse Spiral (NPSS). The choice of the two types of sparse spirals after the transformation is affected remarkably by the boundary effect if a small domain size is applied. Moreover, the boundary effect gives rise to novel meandering of sparse spiral with only outward petals.