Interaction of multi-armed spirals in bistable media

TL;DR

This paper investigates the complex interactions of multi-armed spirals in bistable media modeled by FitzHugh-Nagumo equations, revealing conditions for arm collision, connection, and the resulting dynamic behaviors.

Contribution

It provides a detailed analysis of how initial distances influence spiral interactions and identifies relationships between various oscillation frequencies and model parameters.

Findings

Dense multi-armed spirals exhibit continuous arm collision and reconnection.

The rotation and zigzag frequencies are related through specific model parameters.

Behavior of individual arms matches that of single-armed spirals when initial distances are large.

Abstract

We study the interaction of both dense and sparse multi-armed spirals in bistable media modeled by equations of FitzHugh-Nagumo type. Dense 1-armed spiral is characterized by its fixed tip. For dense multi-armed spirals, when the initial distance between tips is less than a critical value, the arms collide, connect and disconnect continuously as the spirals rotate. The continuous reconstruction between the front and the back drives the tips to corotate along a rough circle and to meander zigzaggedly. The rotation frequency of tip, the frequency of zigzagged displacement, the frequency of spiral, the oscillation frequency of media, and the number of arms satisfy certain relations as long as the control parameters of the model are fixed. When the initial distance between tips is larger than the critical value, the behaviors of individual arms within either dense or sparse multi-armed spirals are identical to that of corresponding 1-armed spirals.