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Noisy consensus dynamics in windmill-type graphs.

Weigang Sun1, Yifan Li1, Suyu Liu1

  • 1Department of Mathematics, School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China.

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Summary
This summary is machine-generated.

This study explores consensus algorithms on noisy windmill graphs, finding that graph structure and leader count significantly impact network coherence and consensus dynamics.

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Area of Science:

  • Network Science
  • Graph Theory
  • Control Theory

Background:

  • Consensus algorithms are crucial for distributed systems.
  • Understanding network coherence in noisy environments is challenging.
  • Windmill graphs offer complex network structures for analysis.

Purpose of the Study:

  • To apply and compare leaderless and leader-follower consensus algorithms.
  • To analyze consensus dynamics on generalized windmill graphs.
  • To investigate the impact of graph structure and leaders on coherence.

Main Methods:

  • Utilized Laplacian spectrum for quantifying coherence.
  • Developed exact solutions for leader-follower coherence.
  • Employed generalized windmill graphs as network models.
  • Compared coherence behaviors of nonisomorphic graphs.

Main Results:

  • Distinct coherence behaviors were observed based on intrinsic graph structures.
  • Exact solutions for leader-follower coherence were derived.
  • Network coherence expressions were explicitly obtained for selected models.

Conclusions:

  • Graph parameters and the number of leaders profoundly influence consensus algorithms.
  • The intrinsic structure of networks dictates coherence properties.
  • Robustness analysis revealed key factors affecting consensus achievement.