Spiking behavior in a noise-driven system combining oscillatory and excitatory properties

Area of Science:

• Computational Neuroscience
• Nonlinear Dynamics
• Mathematical Biology

Background:

• The FitzHugh-Nagumo model is a simplified neuron model exhibiting complex dynamics.
• Understanding the role of noise in neural oscillations is crucial for explaining brain function.
• The canard region near supercritical Hopf bifurcations presents unique dynamical behaviors.

Purpose of the Study:

• To investigate the effect of noise on the regularization of firing activity in the FitzHugh-Nagumo model.
• To identify conditions leading to imperfect phase locking between interspike intervals and quasiharmonic oscillations.
• To demonstrate that this phase locking can arise intrinsically from the model's dynamics.

Main Methods:

• Numerical simulations of the FitzHugh-Nagumo neuron model.
• Analysis of spiking activity and interspike interval variability.
• Bifurcation analysis to identify the canard region.
• Investigation of phase locking phenomena.

Main Results:

• Noise was found to regularize spiking activity in the FitzHugh-Nagumo model operating in the canard region.
• Conditions for imperfect phase locking between interspike intervals and low-amplitude quasiharmonic oscillations were established.
• This imperfect phase locking was shown to be an intrinsic property, not requiring external forcing.

Conclusions:

• Noise can play a constructive role in stabilizing neural firing patterns.
• Intrinsic mechanisms within neuron models can generate complex oscillatory and phase-locking behaviors.
• The FitzHugh-Nagumo model provides a framework for understanding noise-induced regularization and intrinsic phase locking in neural systems.