Optimal system size for complex dynamics in random neural networks near criticality

Area of Science:

• Physics
• Statistical Mechanics
• Complex Systems

Background:

• Dynamical agents coupled via random connectivity matrices are modeled after random neural networks.
• In infinite systems, increasing disorder drives a phase transition to chaotic dynamics.
• Previous work established a link between disorder and chaotic behavior in large-scale networks.

Purpose of the Study:

• Investigate novel phenomena in finite-size systems below the critical disorder threshold.
• Explain the observed system size resonance effect.
• Provide a general framework for understanding this resonance using random matrix theory.

Main Methods:

• Analysis of a dynamical agent model with random connectivity.
• Exploration of the sub-critical regime for finite system sizes.
• Application of extreme value theory to eigenvalues of random matrices.

Main Results:

• A novel phenomenon of system size resonance is observed in finite systems.
• The probability of complex dynamics is maximized at intermediate system sizes when disorder is near criticality.
• A general explanation for this resonance is provided via extreme value theory.

Conclusions:

• Finite system size plays a crucial role in the emergence of complex dynamics.
• System size resonance is a generalizable phenomenon explained by random matrix eigenvalue statistics.
• The findings offer new insights into the behavior of complex networked systems.