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Summary
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Large functional networks can grow stably if load reduction during failures is fast enough. Otherwise, network size stability depends on load reduction speed and network type, with scale-free networks being more resilient.

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Area of Science:

  • Network science
  • Complex systems analysis
  • Systems engineering

Background:

  • Functional networks face risks of cascading overload failures.
  • Understanding stable network growth limits is crucial for system resilience.

Purpose of the Study:

  • To determine the maximum stable size of functional networks under cascading overload failures.
  • To evaluate the impact of load reduction speed on network stability.
  • To compare the stability of scale-free versus exponential networks.

Main Methods:

  • Modeling cascading failures induced by temporally fluctuating loads.
  • Calculating the maximum stable network size (nmax) as a function of the load reduction parameter (r).
  • Analyzing network stability for different network topologies (scale-free and exponential).

Main Results:

  • Infinite network growth is possible if the total load is reduced sufficiently fast (r ≥ rc).
  • A finite maximum stable network size (nmax) exists when load reduction is slow (r < rc), increasing with r.
  • For a fixed slow load reduction (r < rc), scale-free networks exhibit larger maximum stable sizes than exponential networks with the same average degree.

Conclusions:

  • Network resilience to cascading failures is highly dependent on the speed of load reduction.
  • Network topology significantly influences stability, with scale-free networks offering greater robustness.
  • Strategies for detecting and avoiding catastrophic network breakdowns can be informed by understanding the relationship between initial network size and component size post-failure.