Discontinuity-Induced Dynamics in the Conductance-Based Adaptive Exponential Integrate-and-Fire Model

Area of Science:

• Computational neuroscience
• Mathematical modeling of neural dynamics

Background:

• The Conductance-Based Adaptive Exponential (CAdEx) integrate-and-fire model is crucial for understanding neuronal excitability.
• Its dynamics are influenced by multiple timescales, yet the precise mechanisms shaping its regimes remain incompletely understood.

Purpose of the Study:

• To computationally investigate the CAdEx model's multiple timescale nature.
• To elucidate how this feature shapes the model's spiking and delayed bursting regimes.

Main Methods:

• Numerical bifurcation analysis using the COCO software package.
• Detailed examination of discontinuity-induced bifurcations and canard solutions.

Main Results:

• Spiking and delayed bursting regimes are triggered by discontinuity-induced bifurcations linked to multiple timescales.
• Spike-increment transitions occur, accompanied by fold and period-doubling bifurcations, organized along an isola of periodic solutions.
• A homoclinic bifurcation terminating a canard explosion, alongside resets, organizes the delayed bursting regime.

Conclusions:

• The multiple-timescale aspect of the CAdEx model is fundamental to its complex dynamical behaviors.
• Discontinuity-induced bifurcations and canard solutions play a critical role in generating distinct firing patterns.
• This analysis provides a precise mechanistic understanding of the CAdEx model's regimes.