Quantized spiral tip motion in excitable systems with periodic heterogeneities.

Area of Science:

• Chemical kinetics
• Complex systems dynamics
• Pattern formation

Background:

• Reaction-diffusion systems exhibit complex spiral tip dynamics.
• Meandering spiral tips typically show incommensurate radii and frequencies.
• Understanding these dynamics is crucial for various scientific fields.

Purpose of the Study:

• To investigate the transition from incommensurate to commensurate spiral tip dynamics.
• To explore the emergence of a devil's staircase in these systems.
• To characterize the nature of spiral tip orbits under periodic perturbations.

Main Methods:

• Introduction of periodic spatial perturbations into homogeneous reaction-diffusion systems.
• Analysis of spiral tip trajectories and their frequency/radius relationships.
• Identification of devil's staircase structures and their plateaus.

Main Results:

• Periodic perturbations induced a transition to commensurate radii and frequencies.
• A devil's staircase was observed, indicating complex periodic behavior.
• Plateaus on the staircase correspond to pinned or complex periodic orbits.

Conclusions:

• Spatial perturbations offer a method to control spiral tip dynamics.
• The devil's staircase reveals a rich hierarchy of periodic behaviors.
• This study provides insights into the control and characterization of complex patterns.