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Interaction of multiarmed spirals in bistable media.

Ya-feng He¹, Bao-quan Ai, Fu-cheng Liu

¹Hebei Key Laboratory of Optic-electronic Information Materials, College of Physics Science and Technology, Hebei University, Baoding 071002, China. heyf@hbu.edu.cn

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

|June 18, 2013

Summary

Dense multiarmed spirals exhibit complex tip interactions, leading to continuous arm reconstruction and synchronized meandering. When tips are far apart, arms behave independently, mirroring single-arm spiral dynamics.

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Area of Science:

Computational neuroscience
Theoretical physics
Complex systems

Background:

Spiral waves are dynamic patterns observed in excitable media.
FitzHugh-Nagumo models describe the behavior of such systems.
Understanding multiarmed spiral interactions is crucial for complex pattern formation.

Purpose of the Study:

To investigate the interaction dynamics of dense and sparse multiarmed spirals.
To analyze the behavior of spiral wave tips in bistable media.
To identify relationships between spiral dynamics and control parameters.

Main Methods:

Modeling bistable media using FitzHugh-Nagumo equations.
Simulating dense and sparse multiarmed spiral interactions.
Analyzing tip trajectories, rotation frequencies, and oscillation patterns.

Main Results:

Dense multiarmed spirals with close tips show continuous arm collision, connection, and disconnection.
Continuous reconstruction drives synchronized corotation and zigzag meandering of tips.
When initial tip distance exceeds a critical value, arms behave independently, similar to one-armed spirals.

Conclusions:

Spiral tip proximity dictates complex collective behaviors in dense multiarmed systems.
Interactions within multiarmed spirals reveal fundamental principles of pattern formation in excitable media.
The study establishes quantifiable relationships between spiral dynamics and model parameters.