Origin of jumping oscillons in an excitable reaction-diffusion system

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.

Automated summary

The article explains the formation of jumping oscillons through the modulational instability of excitable traveling pulses, and also reveals the existence and stability of bound states of oscillons and pulses, including patches of such states. This rich variety of spatiotemporal states can be utilized for information and storage processing.