An extensive study of two-node McCulloch-pitts networks

Area of Science:

• Computational Neuroscience
• Systems Biology
• Network Science

Background:

• Previous classifications of two-node networks were limited.
• The inclusion of self-loops expands the complexity of signed regulatory graphs to 39 types.

Purpose of the Study:

• To comprehensively summarize the dynamical behaviors of 39 two-node McCulloch-Pitts models.
• To investigate the impact of Boolean variable types (bipolar vs. binary) on network dynamics.
• To analyze three types of robustness (rule, state, and initial state) in these models.

Main Methods:

• Analysis of 39 signed regulatory graphs with link weights {-1, 0, +1}.
• Comparison of dynamics using bipolar [-1,1] and binary [0,1] Boolean node variables.
• Systematic evaluation of model robustness against parameter and initial state changes.

Main Results:

• The number of signed regulatory graphs increases to 39 with self-loops.
• Network dynamics differ between bipolar and binary Boolean variables, even with identical graphs.
• Fixed-point rules exhibit higher stability for parameter changes but lower stability for initial state changes.

Conclusions:

• Slight variations in McCulloch-Pitts models can lead to fundamentally different dynamics.
• Understanding network dynamics and stability is crucial for minimum complex systems.
• The study provides a foundation for analyzing robustness in biological networks.