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

Area of Science:

• Nonlinear dynamics
• Complex systems
• Mathematical modeling

Background:

• Rogue waves are nonlinear phenomena observed across diverse fields, including oceanography, optics, and Bose-Einstein condensates.
• Understanding the mechanisms behind rogue wave formation is crucial for predicting and mitigating their impact.

Purpose of the Study:

• To investigate the emergence of rogue wave-like dynamics in a reaction-diffusion system.
• To analyze the role of subcritical Turing instability in generating these dynamics.
• To characterize the spatiotemporal organization and statistical properties of the observed rogue wave phenomena.

Main Methods:

• Utilizing a reaction-diffusion model exhibiting a subcritical Turing instability.
• Analyzing the system's behavior in a regime where time-independent states are unstable.
• Characterizing the intermittent excitation, collapse, and regrowth of localized spikes.
• Examining the spatiotemporal organization and statistical properties of spike dynamics in varying domain sizes.

Main Results:

• Rogue wave-like dynamics were observed in the reaction-diffusion system.
• These dynamics arise from intermittent localized spikes that collapse and subsequently regrow.
• In sufficiently large domains, the spike dynamics were found to be consistent with a memoryless process.

Conclusions:

• Subcritical Turing instability can lead to rogue wave-like phenomena in reaction-diffusion systems.
• The observed dynamics are characterized by intermittent spiking and regrowth.
• The memoryless nature of these dynamics in large domains provides insights into their statistical behavior.