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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Symmetry induced group consensus.

Isaac Klickstein1, Louis Pecora2, Francesco Sorrentino1

  • 1Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87106, USA.

Chaos (Woodbury, N.Y.)
|August 3, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a novel group consensus method for complex networks, enabling symmetric nodes to reach common states. It allows distinct dynamics for non-symmetric nodes and explores isolated group consensus phenomena.

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Area of Science:

  • Complex Networks
  • Control Theory
  • Multi-agent Systems

Background:

  • Traditional consensus problems focus on a single common final state, which is not always desirable in real-world complex networks.
  • Existing group consensus methods often neglect the underlying network topology.
  • A need exists for consensus strategies that account for network structure and allow for differentiated states among nodes.

Purpose of the Study:

  • To develop a new type of group consensus that leverages network topology.
  • To achieve consensus among symmetric nodes while allowing distinct dynamics for non-symmetric nodes.
  • To investigate the possibility of isolated group consensus within network clusters.

Main Methods:

  • Proposed a simple coupling protocol for heterogeneous linear agents that exploits network topology.
  • Analyzed the dynamic behavior of nodes based on symmetry and network structure.
  • Investigated consensus achievement on both stable and unstable trajectories.

Main Results:

  • Demonstrated successful group consensus for heterogeneous linear agents by exploiting network topology.
  • Showed that group consensus can be achieved on both stable and unstable trajectories.
  • Observed and characterized the phenomenon of 'isolated group consensus,' where specific clusters reach consensus independently.

Conclusions:

  • The proposed coupling protocol effectively achieves a novel form of group consensus in complex networks.
  • Network topology plays a crucial role in enabling differentiated consensus states.
  • The findings open possibilities for controlling complex systems with partial or clustered consensus.