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Set stability and synchronization of generalized asynchronous probabilistic Boolean networks with impulsive effects
Fukun Liu1, Yujie Sun2,3, Chuan Zhang4
1College of Computer Science, Taiyuan University of Technology, Jinzhong, China.
This study introduces a method to verify set stability in generalized asynchronous probabilistic Boolean networks with impulsive effects. The findings enable the analysis of global stability and synchronization in these complex systems.
Area of Science:
- Control Theory
- Network Science
- Dynamical Systems
Background:
- Generalized asynchronous probabilistic Boolean networks (GAPBNs) are crucial for modeling complex systems.
- Impulsive effects introduce transient dynamics that challenge stability analysis.
- Set stability is a key concept for understanding system behavior and predictability.
Purpose of the Study:
- To investigate the set stability of GAPBNs with impulsive effects.
- To develop an efficient algorithm for determining the largest invariant set.
- To establish criteria for global stability and synchronization analysis.
Main Methods:
- Design of an efficient algorithm to find the largest invariant set.
- Derivation of a necessary and sufficient criterion for set stability.
- Verification of global stability and synchronization using selected sets.
Main Results:
- An efficient algorithm for identifying invariant sets in GAPBNs.
- A novel criterion for assessing set stability in systems with impulsive effects.
- Demonstration of global stability and synchronization through case studies.
Conclusions:
- The proposed methods effectively determine set stability for GAPBNs with impulsive effects.
- The criteria facilitate the analysis of global stability and synchronization.
- The findings offer valuable insights for designing and controlling complex asynchronous networks.
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