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Controlling synchronous patterns in complex networks.

Weijie Lin1,2, Huawei Fan2, Ying Wang2

  • 1Department of Physics, Zhejiang University, Hangzhou 310027, China.

Physical Review. E
|May 14, 2016
PubMed
Summary
This summary is machine-generated.

Researchers developed a method to control synchronization patterns in complex networks of chaotic oscillators. By using a small control network and pinning coupling, they can stabilize unstable synchronous patterns based on network symmetries.

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Area of Science:

  • Complex networks
  • Chaos theory
  • Nonlinear dynamics

Background:

  • Complex networks exhibit numerous permutation symmetries, but few lead to stable synchronous patterns.
  • Controlling synchronization in coupled chaotic oscillators is crucial for understanding network dynamics.

Purpose of the Study:

  • To present a general framework for controlling synchronization patterns in complex networks of coupled chaotic oscillators.
  • To develop techniques for stabilizing unstable synchronous patterns based on network symmetries.

Main Methods:

  • Designed a small, weighted control network for pinning coupling to a large complex network.
  • Developed mathematical arguments for the existence of a critical pinning strength to stabilize synchronous patterns.
  • Verified the control method through numerical simulations and experimental demonstrations with chaotic circuits.

Main Results:

  • Demonstrated that a critical pinning strength can stabilize unstable synchronous patterns associated with network symmetries.
  • Successfully controlled synchronization patterns in both artificial and real-world complex networks.
  • Validated the proposed control method experimentally in coupled chaotic circuits.

Conclusions:

  • The proposed pinning coupling method effectively controls synchronization patterns in complex networks of coupled chaotic oscillators.
  • Network permutation symmetries can be leveraged to design effective control strategies for synchronization.
  • This work highlights the controllability of synchronous patterns in complex dynamical networks.