Tracking target and spiral waves

Area of Science:

• Chemical kinetics
• Pattern formation in chemical systems
• Nonlinear dynamics

Background:

• Spiral and target waves are complex spatio-temporal patterns observed in chemical reactions.
• Analyzing the dynamics and evolution of these waves is crucial for understanding reaction-diffusion systems.
• Existing methods often rely on identifying the spiral tip, which can be challenging in complex systems.

Purpose of the Study:

• Introduce a new algorithm for analyzing spiral and target wave evolution in chemical systems.
• Develop a method to locate the center of wave patterns using the concept of a spiral focus.
• Investigate the movement and correlation of these foci in experimental data.

Main Methods:

• Developed a novel algorithm based on the concept of a spiral focus, defined by the evolutes of waves.
• Employed Gaussian smoothing for robust identification of target and spiral foci, independent of wave profile.
• Applied the algorithm to analyze long image sequences from Belousov-Zhabotinsky reaction experiments.

Main Results:

• Successfully identified moving target and spiral foci in experimental data.
• Quantified the speed and direction of movement for single and double spiral foci.
• Observed that focus movement correlates with neighboring foci, irrespective of their origin.

Conclusions:

• The spiral focus concept provides a robust alternative to spiral tip identification for analyzing wave patterns.
• The developed algorithm enables detailed investigation of wave dynamics and interactions.
• Focus movement in chemical systems exhibits local correlations, offering insights into pattern evolution.