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This study analyzes synchronization in output-coupled temporal Boolean networks (TBNs) with differing state and output delays. New conditions ensure array synchronization, demonstrated with an epigenetic model.

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Area of Science:

  • Systems Biology
  • Theoretical Computer Science
  • Control Theory

Background:

  • Temporal Boolean networks (TBNs) model biological systems with regulatory delays.
  • Understanding synchronization in coupled TBNs is crucial for complex system analysis.
  • Distinguishing between state and output delays presents unique modeling challenges.

Purpose of the Study:

  • To analytically investigate synchronization phenomena in arrays of output-coupled TBNs.
  • To develop conditions for achieving synchronization in TBN systems with distinct state and output delays.
  • To validate the theoretical findings using numerical examples, including a biological model.

Main Methods:

  • Utilizing algebraic representations of logical dynamics.
  • Employing the semi-tensor product of matrices for system conversion.
  • Deriving necessary and sufficient conditions for synchronization.

Main Results:

  • Output-coupled TBNs are transformed into a discrete-time algebraic evolution system.
  • The relationship between coupled TBN states and initial state sequences is established.
  • Novel conditions for the synchronization of TBN arrays are derived.

Conclusions:

  • The study provides a robust analytical framework for TBN synchronization.
  • The derived conditions offer precise criteria for controlling TBN array behavior.
  • The findings are applicable to modeling and controlling complex biological networks.