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Adaptive pinning cluster synchronization of a stochastic reaction-diffusion complex network.

Binglong Lu1, Haijun Jiang2, Cheng Hu2

  • 1School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, 466001, Henan, China.

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|August 14, 2023
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Summary
This summary is machine-generated.

This study demonstrates novel pinning control strategies to achieve cluster synchronization in complex networks with reaction-diffusion dynamics, directed coupling, noise, and switching. Adaptive controllers automatically adjust gains for efficient synchronization without needing isolated node targets.

Keywords:
Adaptive pinning controlCluster synchronizationMarkovian switchingReaction–diffusion complex networkStochastic noise

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Area of Science:

  • Complex Networks
  • Nonlinear Dynamics
  • Control Theory

Background:

  • Complex networks exhibit phenomena like reaction-diffusion and directed coupling.
  • Stochastic noise and Markovian switching introduce significant challenges in network dynamics.
  • Achieving synchronized behavior in such intricate systems is a key research area.

Purpose of the Study:

  • To achieve cluster synchronization in complex networks under challenging conditions.
  • To develop and analyze novel pinning control strategies for synchronization.
  • To investigate adaptive control mechanisms that adjust gains automatically.

Main Methods:

  • Proposed switched constant gain pinning, centralized adaptive pinning, and decentralized adaptive pinning controllers.
  • Utilized adaptive controllers where control gain and coupling strength adjust automatically.
  • Defined cluster synchronization target as the average state within a cluster, considering directed topology.

Main Results:

  • Successfully demonstrated cluster synchronization in directed coupled reaction-diffusion neural networks.
  • Adaptive pinning controllers proved effective in achieving synchronization with partial node control.
  • The proposed target state definition simplifies synchronization requirements.

Conclusions:

  • The developed pinning control strategies are effective for achieving cluster synchronization in complex, disturbed networks.
  • Adaptive control offers an efficient approach by automatically tuning parameters.
  • The study advances synchronization theory for networks with realistic complexities.