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Stability of large-scale probabilistic Boolean networks via network aggregation.

Wen Liu1, Shihua Fu2, Jianjun Wang2

  • 1School of Science and Technology, University of Camerino, Camerino, 62032, Italy; School of Mathematical Sciences, Liaocheng University, Liaocheng,252026, PR China.

Neural Networks : the Official Journal of the International Neural Network Society
|September 18, 2025
PubMed
Summary

This study introduces network aggregation for large-scale probabilistic Boolean networks (LSPBNs), significantly reducing computational complexity. The proposed method establishes a sufficient condition for global stability in these complex systems.

Keywords:
Large-scale systemsNetwork aggregationProbabilistic Boolean networkSemi-tensor productStability

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Area of Science:

  • Computational Biology
  • Systems Biology
  • Network Science

Background:

  • Large-scale probabilistic Boolean networks (LSPBNs) are valuable for simulating complex systems with uncertainty.
  • High computational complexity limits the direct application of existing research methods to LSPBNs.
  • Network aggregation offers a potential solution to overcome these computational challenges.

Purpose of the Study:

  • To investigate the global stability of LSPBNs using network aggregation.
  • To develop a computationally efficient method for analyzing LSPBN dynamics.
  • To ensure the stability conclusion is applicable across various network aggregation forms.

Main Methods:

  • Partitioning the LSPBN into subnetworks.
  • Utilizing the semi-tensor product of matrices to derive algebraic expressions for subnetworks.
  • Constructing iterative formulas to model inter-subnetwork coordination.
  • Deriving a sufficient condition for global stability based on these formulas.

Main Results:

  • A novel network aggregation approach for LSPBNs is presented.
  • Iterative formulas effectively capture input-output relationships among subnetworks.
  • A sufficient condition for the global stability of LSPBNs is derived.
  • Computational complexity is substantially reduced compared to traditional methods.

Conclusions:

  • The proposed network aggregation method provides an efficient way to analyze LSPBN global stability.
  • The derived stability condition is robust and applicable to any form of network aggregation.
  • The method's feasibility is confirmed through illustrative examples.