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Synchronization of complex dynamical networks via impulsive control.

Gang Zhang1, Zengrong Liu, Zhongjun Ma

  • 1Department of Mathematics, Shijiazhuang College, Shijiazhuang, 050035, China.

Chaos (Woodbury, N.Y.)
|January 1, 2008
PubMed
Summary

This study introduces an impulsive control method for achieving synchronization in complex dynamical networks with unknown coupling. The strategy leverages node weights to enable synchronization using only a few key nodes, demonstrated with the chaotic Chua system.

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Area of Science:

  • Complex Systems
  • Control Theory
  • Network Science

Background:

  • Synchronization is crucial for complex dynamical networks.
  • Controlling synchronization in networks with unknown coupling is challenging.

Purpose of the Study:

  • To propose an impulsive control scheme for achieving synchronization in complex dynamical networks with unknown coupling.
  • To demonstrate that synchronization can be achieved with a few selected nodes by adjusting their weights.

Main Methods:

  • Utilized stability theory for impulsive differential equations.
  • Developed an impulsive control strategy considering node influence and weights.
  • Employed the chaotic Chua system for simulation.

Main Results:

  • Successfully achieved impulsive synchronization in complex dynamical networks.
  • Showcased that effective synchronization is possible by selecting and weighting a subset of nodes.
  • Validated the proposed impulsive control scheme's effectiveness through simulations.

Conclusions:

  • The proposed impulsive control scheme is effective for achieving synchronization in complex dynamical networks.
  • Node weighting offers a practical approach to reduce control complexity by using fewer nodes.
  • The method is robust and applicable to systems like the chaotic Chua network.