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Leader-follower consensus on activity-driven networks.

Jalil Hasanyan1, Lorenzo Zino1, Daniel Alberto Burbano Lombana1

  • 1Department of Mechanical and Aerospace Engineering, New York University Tandon School of Engineering, Brooklyn, NY, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
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PubMed
Summary
This summary is machine-generated.

Group leaders help social animals reach beneficial consensus. Surprisingly, individual differences (heterogeneity) can speed up group decision-making, improving collective performance in animal and human groups.

Keywords:
consensusleader–followermean-squareopinion dynamicsperturbationtime-varying

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Area of Science:

  • Collective dynamics
  • Social network analysis
  • Mathematical biology

Background:

  • Social groups exhibit collective behaviors modulated by leaders for consensus.
  • Leaders facilitate group decision-making for survival and resource acquisition.
  • Understanding leader-follower dynamics is crucial for group efficiency.

Purpose of the Study:

  • To investigate a stochastic leader-follower consensus problem with perceptual constraints.
  • To analyze how individual differences in social connection tendencies affect group consensus.
  • To provide theoretical conditions for consensus protocol stability and convergence rate.

Main Methods:

  • Stochastic stability theory
  • Eigenvalue perturbation theory
  • Mean-square analysis of consensus protocols

Main Results:

  • Necessary and sufficient conditions for asymptotic stability were derived.
  • Closed-form estimates for the convergence rate were obtained.
  • A minimalistic model surprisingly predicted observed group behaviors.

Conclusions:

  • Heterogeneity can counterintuitively benefit group decision-making by enhancing consensus convergence rate.
  • Inter-individual variability improves group performance, supported by studies on social insects and human teams.
  • The findings offer insights into optimizing collective behavior in diverse social systems.