Origin of Jumping Oscillons in an Excitable Reaction-Diffusion System

TL;DR

This paper investigates the origin of jumping oscillons in an excitable reaction-diffusion system, revealing their creation through modulational instability of traveling pulses and exploring their complex interactions and stability.

Contribution

It introduces a bifurcation-based explanation for jumping oscillons and uncovers their bound states and stability properties in a reaction-diffusion model.

Findings

Jumping oscillons originate from modulational instability of traveling pulses.

Bound states of oscillons and traveling pulses are identified and analyzed.

The system exhibits diverse stable spatiotemporal patterns with potential information storage applications.

Abstract

Oscillons, i.e., immobile spatially localized but temporally oscillating structures, are the subject of intense study since their discovery in Faraday wave experiments. However, oscillons can also disappear and reappear at a shifted spatial location, becoming jumping oscillons (JOs). We explain here the origin of this behavior in a three-variable reaction-diffusion system via numerical continuation and bifurcation theory, and show that JOs are created via a modulational instability of excitable traveling pulses (TPs). We also reveal the presence of bound states of JOs and TPs and patches of such states (including jumping periodic patterns) and determine their stability. This rich multiplicity of spatiotemporal states lends itself to information and storage handling.