Transient dynamics for sequence-processing neural networks: effect of degree distributions.

Area of Science:

• Computational neuroscience
• Network science
• Theoretical physics

Background:

• Sequence processing neural networks are crucial for understanding brain function.
• Network topology significantly influences neural network dynamics.
• Existing models often lack detailed analysis of degree distribution effects.

Purpose of the Study:

• To derive an analytic evolution equation for overlap parameters in neural networks.
• To investigate the impact of degree distribution on transient dynamics.
• To predict critical loading ratios in different network structures.

Main Methods:

• Derivation of an analytic evolution equation for overlap parameters.
• Analysis of transient dynamics incorporating degree distribution effects.
• Comparison of theoretical predictions with numerical experiments.

Main Results:

• An analytic evolution equation for overlap parameters was successfully derived.
• The critical loading ratio alpha_{c}=N;{-12} was precisely obtained for globally coupled networks.
• Theoretical predictions showed quantitative agreement with numerical experiments for delta, binomial, and power-law degree distributions.

Conclusions:

• The derived equation provides a powerful tool for analyzing neural network dynamics.
• Degree distribution is a key factor influencing transient dynamics and critical loading ratios.
• The model offers accurate predictions across various random network topologies.