Origin of Jumping Oscillons in an Excitable Reaction-Diffusion System

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.

arXiv comment5 pages, 3 figures, supplementary material (3 pages, 5 figures)

References in corpus (5)

• Generation of finite wave trains in excitable media
• Dispersive instabilities in Passively Mode-Locked Integrated External-Cavity Surface-Emitting Lasers
• Two-dimensional localized states in an active phase-field-crystal model
• Periodic orbit analysis of a system with continuous symmetry - a tutorial
• Molding the asymmetry of localized frequency-locking waves by a generalized forcing and implications to the inner ear

Cited by in corpus (5)

• Stationary broken parity states in active matter models
• Amplitude equations for wave bifurcations in reaction-diffusion systems
• Instability mechanisms of repelling peak solutions in a multi-variable activator-inhibitor system
• Emergence of rogue-like waves in a reaction-diffusion system: Stochastic output from deterministic dissipative dynamics
• From Order to Chimeras: Unraveling Dynamic Patterns in Active Fluids with Nonlinear Growth