Greater accuracy and broadened applicability of phase reduction using isostable coordinates.

Area of Science:

• Dynamical systems theory
• Nonlinear dynamics
• Computational biology

Background:

• Phase models are limited to weak perturbations near periodic orbits.
• Existing models struggle with dynamics away from the limit cycle.

Purpose of the Study:

• To develop a corrected phase reduction method for analyzing perturbed oscillators.
• To extend the applicability of phase models to larger perturbations and complex systems.

Main Methods:

• Utilized isostables of periodic orbits to define a simplified coordinate system.
• Devised a strategy to correct phase dynamics for locations away from the limit cycle.
• Formulated a closed set of equations applicable to high-dimensional systems.

Main Results:

• Corrected phase dynamics allow for larger perturbation magnitudes.
• Improved optimal control strategies for modifying oscillation periods.
• Enabled analysis of adaptation and memory effects in biological models.

Conclusions:

• The corrected phase reduction method expands the utility of phase models.
• This approach offers new insights into biological system dynamics and control.