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Selection mechanism for rotating patterns in weakly excitable media.

Vladimir S Zykov¹

¹Institut für Theoretische Physik, Technische Universität Berlin, D-10623 Berlin, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 16, 2007

Summary

This study explores rotating patterns in excitable media, revealing a selection mechanism that dictates pattern shape and speed. These patterns, including boundary spots and central spirals, coexist or disappear based on medium properties and disk size.

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Area of Science:

Complex Systems
Nonlinear Dynamics
Pattern Formation in Excitable Media

Background:

Excitable media exhibit complex spatiotemporal dynamics, including pattern formation.
Understanding pattern selection and stability in confined geometries is crucial for various scientific fields.

Purpose of the Study:

To investigate two distinct rigidly rotating patterns within a disk of a weakly excitable medium.
To identify the selection mechanism governing the shape and angular velocity of these patterns.
To analyze the coexistence, bifurcation, and disappearance of these patterns based on medium excitability and disk radius.

Main Methods:

Utilized the free-boundary approach to model and analyze the rotating patterns.
Investigated the influence of medium excitability and disk radius on pattern dynamics.

Main Results:

Identified two coexisting patterns: boundary-moving spots and center-rotating spiral waves.
Discovered a selection mechanism that uniquely determines pattern shape and angular velocity.
Established conditions for pattern coexistence, bifurcation, and non-existence based on critical parameter values.

Conclusions:

The free-boundary approach successfully describes pattern selection in confined excitable media.
A unified selection mechanism governs both boundary and spiral wave patterns.
The findings are applicable to spiral waves in unbounded media as a limiting case.