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Local Synchronization of Interconnected Boolean Networks With Stochastic Disturbances
IEEE Transactions on Neural Networks and Learning Systems
|April 17, 2019
Summary
This study addresses local synchronization in interconnected Boolean networks (BNs), both with and without stochastic disturbances. New criteria and algorithms are presented for analyzing synchronization and calculating the domain of attraction.
Area of Science:
- Control Theory
- Network Science
- Computer Science
Background:
- Interconnected Boolean networks (BNs) are crucial for modeling complex systems.
- Understanding their synchronization behavior is vital for system stability and control.
- Stochastic disturbances can significantly impact network dynamics.
Purpose of the Study:
- To investigate the local synchronization problem in interconnected Boolean networks.
- To develop methods for analyzing synchronization in the presence and absence of stochastic disturbances.
- To design algorithms for calculating the domain of attraction for synchronization.
Main Methods:
- Analysis of reachable sets and limit sets for global initial states.
- Utilizing logical submatrices of Boolean vectors for algebraic expressions.
- Introduction of random logical variables to model stochastic disturbances.
- Derivation of necessary and sufficient conditions for local synchronization.
Main Results:
- A compact algebraic expression for the limit set of interconnected BNs.
- Established local synchronization criteria for BNs with and without stochastic disturbances.
- Developed efficient algorithms to compute the largest domain of attraction.
- Demonstrated the effectiveness of the proposed methods through numerical examples.
Conclusions:
- The study provides a comprehensive framework for analyzing local synchronization in interconnected Boolean networks.
- The developed criteria and algorithms are effective for both deterministic and stochastic network models.
- This research contributes to the robust control and analysis of complex networked systems.
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