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Asymptotic Stability of Delayed Boolean Networks With Random Data Dropouts
IEEE Transactions on Neural Networks and Learning Systems
|August 15, 2023
Summary
This study addresses communication limits in Boolean networks (BNs) by modeling time delays and random data loss. A new method ensures network stability despite these constraints, providing a convergence rate.
Area of Science:
- Computer Science
- Network Science
- Control Theory
Background:
- Real-world networks face inevitable communication constraints, including information delays and data packet loss.
- Boolean networks (BNs) are widely used to model complex systems but are sensitive to communication imperfections.
Purpose of the Study:
- To investigate the asymptotic stability of Boolean networks (BNs) with both time delays and randomly missing data.
- To propose a novel data-sending rule that accounts for these communication constraints.
Main Methods:
- Modeling data packet dropout using Bernoulli random variables for each node.
- Representing time delays and missing data with independent random variables.
- Developing an augmented system incorporating current states, delayed information, and transmitted data.
- Utilizing the semitensor product (STP) for theoretical analysis.
Main Results:
- Deriving the necessary and sufficient condition for the asymptotic stability of delayed BNs with random data dropouts.
- Obtaining the convergence rate of the network under these conditions.
Conclusions:
- The proposed methods effectively analyze and ensure the stability of Boolean networks facing realistic communication constraints.
- The findings provide a theoretical framework for designing robust distributed systems with delayed and unreliable communication.
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