Emergence of rogue-like waves in a reaction-diffusion system: Stochastic output from deterministic dynamics

Author:

Edgar Knobloch, Arik Yochelis

Keyword:

Nonlinear Sciences, Pattern Formation and Solitons, Pattern Formation and Solitons (nlin.PS)

journal:

date:

2024-02-28 00:00:00

Abstract

Rogue waves are an intriguing nonlinear phenomenon arising across different scales, ranging from ocean waves through optics to Bose-Einstein condensate. We describe the emergence of rogue wave-like dynamics in a reaction-diffusion system that arise as a result of a subcritical Turing instability. This state is present in the regime where all time-independent states are unstable, and consists of intermittent excitation of spatially localized spikes, followed by collapse to an unstable state and subsequent regrowth. We characterize the spatiotemporal organization of spikes and show that in sufficiently large domains the dynamics are consistent with a memoryless process.

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