Damage spreading and criticality in finite random dynamical networks

Area of Science:

• Network science
• Statistical physics
• Complex systems

Background:

• Damage spreading is crucial for understanding information and failure propagation in technological and natural networks.
• The sparse percolation (SP) limit is a key regime for studying these phenomena.
• Previous studies often relied on approximations that may not hold for finite-sized networks.

Purpose of the Study:

• To systematically compare damage spreading in random Boolean and threshold networks at the SP limit.
• To identify critical connectivity thresholds governing damage propagation.
• To investigate the influence of network size on damage spreading dynamics.

Main Methods:

• Finite-size scaling analysis was employed to study network behavior.
• Perturbations independent of network size (N) were used.
• Marginal damage spreading principles were applied to determine critical connectivity.

Main Results:

• A novel characteristic connectivity (Ks) was identified, where average damage is independent of network size N.
• The critical connectivity at the SP limit for finite N, Kc(sparse)(N), systematically deviates from annealed approximation results.
• These deviations persist even for large system sizes.

Conclusions:

• The findings offer a more accurate understanding of damage spreading dynamics in sparse networks.
• Results may explain observations in biological systems like gene regulatory networks.
• Implications for the evolution of dynamical networks designed for specific functions are significant.