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Set stability and synchronization of generalized asynchronous probabilistic Boolean networks with impulsive effects.

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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.

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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.