Adaptive exponential integrate-and-fire model with fractal extension

Area of Science:

• Neuroscience
• Computational Neuroscience
• Mathematical Biology

Background:

• Mathematical models are crucial for understanding neuronal electrophysiology.
• The Adaptive Exponential Integrate-and-Fire (Adex) model is a widely used tool for simulating neuronal behavior.
• Standard Adex models utilize integer-order derivatives.

Purpose of the Study:

• To propose and investigate a fractal extension of the Adex neuron model.
• To explore the impact of fractal derivatives on neuronal firing patterns and mean frequency.
• To determine if fractal derivatives offer a more realistic neuronal representation.

Main Methods:

• Replaced integer-order derivatives in the Adex model with fractal derivatives.
• Analyzed the effects of using equal and different orders of fractal derivatives.
• Examined changes in inter-spike intervals and mean firing frequency.

Main Results:

• The order of fractal derivatives significantly influences neuronal firing patterns.
• Fractal orders affect the inter-spike intervals and the mean firing frequency of the neuron.
• Firing patterns are dependent on both neuronal parameters and fractal operator orders.

Conclusions:

• The fractal extension of the Adex model provides a generalized framework for neuronal modeling.
• Fractal derivatives offer a nuanced approach to describing neuronal electrophysiology.
• Fractal orders below unity enhance the influence of the adaptation mechanism on spike firing patterns.