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Inner synchronization of controlled multi-valued logical networks.

Yunyun Deng1,2, Xiaolong Qi1,2, Yi Liang1,2,3

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This study introduces a driving node to achieve inner synchronization in multi-valued logical networks. It establishes conditions for nodes to synchronize with the driving node or each other.

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Area of Science:

  • Control Theory
  • Network Science
  • Discrete Mathematics

Background:

  • Multi-valued logical networks are complex systems with applications in various fields.
  • Achieving synchronized states in these networks is crucial for their reliable operation.
  • Existing synchronization methods may not cover all scenarios, necessitating further research.

Purpose of the Study:

  • To investigate and establish conditions for inner synchronization in multi-valued logical networks.
  • To introduce a novel approach using an external driving node to control network synchronization.
  • To develop both specific and general models for achieving inner synchronization.

Main Methods:

  • Utilizing the semi-tensor product to establish synchronization conditions.
  • Developing a specific inner synchronization model where all nodes match the driving node's state.
  • Extending the model to a more general case where nodes synchronize with each other.

Main Results:

  • A necessary and sufficient condition for inner synchronization with the driving node was derived.
  • Criteria for a more general inner synchronization scenario were theoretically established.
  • Simulation examples confirmed the validity of the derived conditions and criteria.

Conclusions:

  • The proposed driving node method effectively facilitates inner synchronization in multi-valued logical networks.
  • The study provides robust theoretical frameworks for analyzing and achieving synchronization.
  • The findings are applicable to the design and control of complex logical networks.