Bifurcation analysis of a Morris-Lecar neuron model

Area of Science:

• Computational neuroscience
• Mathematical modeling of neural dynamics

Background:

• The Morris-Lecar model is a simplified mathematical representation of neuronal activity.
• Understanding neuronal excitability and firing patterns is crucial in neuroscience.

Purpose of the Study:

• To investigate the complex dynamical behaviors of the Morris-Lecar neuron model.
• To analyze the global bifurcation structure and identify conditions for different neuronal behaviors.

Main Methods:

• Utilized bifurcation analysis and numerical simulations.
• Constructed two-parameter bifurcation diagrams (stimulating current vs. other parameters).
• Generated one-parameter bifurcation diagrams and frequency-current curves.

Main Results:

• Identified conditions leading to periodic solutions and bistability.
• Characterized different types of membrane excitability through bifurcation analysis.
• Demonstrated how alterations in membrane properties affect neuronal dynamics.

Conclusions:

• The study provides a comprehensive map of the Morris-Lecar model's dynamics.
• Bifurcation analysis reveals key mechanisms underlying neuronal excitability and pattern generation.