Pattern formation in a 2-population homogenized neuronal network model

Area of Science:

• Computational Neuroscience
• Mathematical Biology
• Neural Field Theory

Background:

• Neural field models are crucial for understanding large-scale brain activity.
• Homogenized models simplify complex neural interactions.
• Periodic microstructures introduce heterogeneity in neural connectivity.

Purpose of the Study:

• To analyze pattern formation in a 2-population homogenized neural field model with periodic microstructure.
• To investigate the role of modulated connectivity functions and spatial scales.
• To understand the influence of firing rate regimes on pattern development.

Main Methods:

• Utilized a 1D Hopfield-type neural field model.
• Employed stability analysis based on wave-number dependent invariants.
• Performed numerical simulations for nonlinear regime analysis.
• Investigated pattern formation across different heterogeneity parameters.

Main Results:

• Nonlocal synaptic interactions induce finite bandwidth instability.
• Instability structure comprises well-separated gain bands.
• Pattern formation depends on firing rate (steep vs. shallow) and kernel localization.
• Weakly modulated regimes yield stable spatial oscillations (steep) or spatiotemporal oscillations (shallow).

Conclusions:

• The study elucidates the mechanisms of pattern formation in heterogeneous neural fields.
• Firing rate and connectivity localization critically determine emergent patterns.
• Results provide insights into how microstructure influences neural dynamics.