Phase reduction for FitzHugh-Nagumo neuron with large timescale separation

Area of Science:

• Computational Neuroscience
• Dynamical Systems Theory

Background:

• Limit-cycle oscillators are crucial in modeling biological systems, including neurons.
• Dimensionality reduction techniques like phase reduction are vital for analyzing complex oscillatory models.
• The FitzHugh-Nagumo model is a simplified yet powerful model of neuronal excitability.

Purpose of the Study:

• To apply the phase reduction approach to the FitzHugh-Nagumo neuron model with significant timescale separation.
• To quantify the oscillator's response to external perturbations by analyzing phase sensitivity functions.
• To investigate the impact of different perturbation types (periodic pulse train, common noise) on synchronization.

Main Methods:

• Utilizing the phase reduction method to simplify the FitzHugh-Nagumo model dynamics.
• Deriving and analyzing the asymptotic behaviors of phase sensitivity functions for fast and slow variables.
• Performing theoretical and numerical investigations of periodic pulse train and common noise perturbations.
• Examining synchronization behaviors under varying perturbation conditions.

Main Results:

• The phase of the FitzHugh-Nagumo oscillator is largely insensitive to perturbations on the fast variable, except at specific jump points.
• Phase sensitivity functions were obtained to quantitatively assess responses to external stimuli.
• Perturbations applied to the slow variable demonstrated superior synchronization performance compared to fast variable perturbations, especially with large timescale separation.

Conclusions:

• The phase reduction approach effectively simplifies the FitzHugh-Nagumo model, revealing key dynamics.
• Understanding phase sensitivity is critical for predicting oscillator responses to external perturbations.
• Targeting perturbations on the slow variable offers a more effective strategy for achieving synchronization in neuron models with large timescale separation.