Analysis of input-induced oscillations using the isostable coordinate framework

Area of Science:

• Dynamical Systems Theory
• Nonlinear Dynamics
• Computational Neuroscience

Background:

• Reduced order modeling is crucial for analyzing complex oscillatory systems.
• Existing methods often fail for oscillations induced by external inputs or coupling.
• Input-induced oscillations are prevalent in biological and physical systems.

Purpose of the Study:

• To develop a robust framework for reduced order modeling of input-induced oscillations.
• To accurately predict bifurcations and phase-locking in coupled dynamical systems.
• To extend these techniques to systems relevant to circadian and neural physiology.

Main Methods:

• Leveraging the isostable coordinate framework for high-accuracy model reduction.
• Employing asymptotic expansion of isostable coordinate dynamics near Hopf bifurcations.
• Utilizing an adaptive phase-amplitude reduction for excitable systems.

Main Results:

• Successfully identified reduced equations for input-induced oscillations.
• Predicted coupling-induced bifurcations leading to stable oscillations.
• Accurately determined steady-state phase-locking relationships.

Conclusions:

• The proposed isostable coordinate framework effectively models input-induced oscillations.
• The methods are applicable to diverse coupled dynamical systems, including those in physiology.
• This work advances the analysis of oscillations in systems driven by external factors.