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<p>This paper studies the emergent dynamics of a flock with nonlinear inherent dynamics under closest neighbors model. We establish sufficient frameworks for convergence to flocking in terms of initial state and system parameters. When the number of closest neighbors is at least half of the population, it is shown that convergence to flocking occurs regardless of the initial state provided that the Lipschitz constant of nonlinear dynamics is smaller than the coupling strength. In contrast, when this number of closest neighbors is less than half of the population, we need to impose some restrictive conditions on the initial state to ensure the emergence of flocking based on the disturbed graphs approach. Our results are applicable to both continuous and discrete time cases. Finally, the validity of our theoretical analysis is tested by numerical simulations.</p>

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Emergent behavior of closest neighbors model with nonlinear inherent dynamics

  • 期刊论文

  • 发表日期：

    2025年4月8日

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  • Yuan Liang,
  • Chen Wu,
  • Jiugang Dong

摘要

This paper studies the emergent dynamics of a flock with nonlinear inherent dynamics under closest neighbors model. We establish sufficient frameworks for convergence to flocking in terms of initial state and system parameters. When the number of closest neighbors is at least half of the population, it is shown that convergence to flocking occurs regardless of the initial state provided that the Lipschitz constant of nonlinear dynamics is smaller than the coupling strength. In contrast, when this number of closest neighbors is less than half of the population, we need to impose some restrictive conditions on the initial state to ensure the emergence of flocking based on the disturbed graphs approach. Our results are applicable to both continuous and discrete time cases. Finally, the validity of our theoretical analysis is tested by numerical simulations.