Dynamical density delay maps: simple, new method for visualising the behaviour of complex systems.

Area of Science:

• Physiology
• Complex Systems Analysis
• Data Visualization

Background:

• Physiological signals like cardiac interbeat intervals display complex fluctuations.
• Conventional time series graphical representations may not capture critical dynamical properties such as nonstationarities.

Purpose of the Study:

• Introduce a novel visualization method, the dynamical density delay mapping (D3-Map) technique.
• Provide an animated representation of a system's dynamics for enhanced data exploration.

Main Methods:

• Generalize conventional 2D Poincaré plots to create animated 3D Poincaré surfaces.
• Map relative frequency of data points onto a color scheme for visualization.
• Generate colorized 2D contour plots and animate original time series graphs with these visualizations.

Main Results:

• Demonstrate D3-Map using cardiac interbeat interval time series from a healthy subject.
• Uncover complex dynamical changes, including state transitions and time spent in each state.
• Illustrate utility in detecting hidden temporal patterns in atrial fibrillation heart rate dynamics.

Conclusions:

• Density delay map animations offer a novel visualization for complex system dynamics.
• The method aids in understanding concepts like nonstationarity and multistability.
• Facilitates data exploration for researchers and serves as an educational tool for trainees.