Rotating spiral waves with phase-randomized core in nonlocally coupled oscillators.

Area of Science:

• Chemical kinetics
• Nonlinear dynamics
• Pattern formation

Background:

• Reaction-diffusion systems commonly exhibit spiral waves.
• Phase-randomized oscillators can disrupt normal spiral wave behavior.
• Diffusion-free components introduce unique dynamics not seen in standard models.

Purpose of the Study:

• To investigate the emergence of rotating spiral waves with phase-randomized cores in reaction-diffusion systems.
• To elucidate the role of diffusion-free components and effective nonlocality in anomalous spiral dynamics.
• To develop a theoretical framework for understanding these phenomena.

Main Methods:

• Utilized a paradigmatic three-component reaction-diffusion model.
• Performed mathematical analysis, particularly in the weak coupling regime.
• Employed the phase reduction method and derived a functional self-consistency equation.
• Conducted numerical simulations to validate theoretical predictions.

Main Results:

• Demonstrated the formation of rotating spiral waves with phase-randomized cores when components are diffusion-free.
• Identified effective nonlocality in coupling as the origin of anomalous spiral dynamics.
• Estimated a critical coupling strength for the onset of this phenomenon.
• Achieved excellent agreement between theoretical predictions and numerical simulations for oscillator frequencies.

Conclusions:

• Diffusion-free components can lead to novel spiral wave patterns in reaction-diffusion systems.
• Effective nonlocality, particularly at weak coupling, is key to anomalous spiral dynamics.
• The derived functional self-consistency equation accurately describes the system's behavior.