Population equations for degree-heterogenous neural networks.

Area of Science:

• Computational Neuroscience
• Statistical Physics
• Network Science

Background:

• Recurrent neural networks exhibit complex dynamics influenced by synaptic connectivity.
• Understanding population-averaged firing rates is crucial for characterizing network behavior.
• Recent findings highlight subnetworks of highly active neurons with preferential interconnections.

Purpose of the Study:

• To develop a statistical framework for analyzing recurrent networks with broad distributions of synaptic links.
• To derive population-averaged firing rates based on neuronal input degrees.
• To investigate the impact of degree-correlated topology on network dynamics.

Main Methods:

• Statistical framework development for recurrent networks.
• Derivation of a system of equations for population-averaged firing rates.
• Application of the theory to networks with degree-correlated topology.

Main Results:

• Analytical solutions for binary neurons reveal step-like activity patterns.
• Complex, multi-stable network regimes emerge with increasing degree correlations.
• The framework accounts for broad distributions of synaptic links per neuron.

Conclusions:

• The developed statistical framework provides insights into the behavior of complex recurrent networks.
• Degree-correlated topology can lead to intricate and multi-stable network states.
• The findings are relevant for understanding neuronal activity in biological networks.