Threshold disorder as a source of diverse and complex behavior in random nets.

Area of Science:

• Computational neuroscience
• Complex systems theory
• Network dynamics

Background:

• Random synchronous asymmetric neural networks (RSANNs) typically exhibit a limited repertoire of complex spatio-temporal patterns.
• Parameter stability in these networks often leads to a small, albeit complex, set of behaviors.

Purpose of the Study:

• To investigate the impact of disordered threshold values on the diversity and complexity of limit-cycle patterns in RSANNs.
• To explore how threshold disorder can expand the behavioral repertoire of RSANNs.
• To identify conditions for achieving a large set of complex patterns for processing applications.

Main Methods:

• Analysis of limit-cycle diversity and complexity in RSANNs with varying degrees of threshold disorder.
• Characterization of pattern repertoire size as a function of threshold disorder magnitude.
• Investigation of pattern simplicity changes with increasing disorder.

Main Results:

• RSANNs with uniform thresholds display a surprisingly small and stable repertoire of complex limit-cycle patterns.
• Introducing threshold disorder above a critical level causes a rapid, power-law increase in pattern repertoire size.
• Further increases in disorder lead to simpler patterns, eventually resulting in fixed points.

Conclusions:

• Threshold disorder is a key factor in diversifying complex behaviors in RSANNs.
• Moderate threshold disorder enables access to a large set of complex patterns, beneficial for rapid processing systems.
• These findings offer insights into controlling and enhancing the behavioral complexity of neural networks and other complex systems.