Authors

Birgit Jacob, Claudia Totzeck

Abstract

We derive a minimal port-Hamiltonian formulation of a general class of interacting particle systems driven by alignment and potential-based force dynamics which include the Cucker-Smale model with potential interaction and the second order Kuramoto model. The port-Hamiltonian structure allows to characterize conserved quantities such as Casimir functions as well as the long-time behaviour using a LaSalle-type argument on the particle level. It is then shown that the port-Hamiltonian structure is preserved in the mean-field limit and an analogue of the LaSalle invariance principle is studied in the space of probability measures equipped with the 2-Wasserstein-metric. The results on the particle and mean-field limit yield a new perspective on uniform stability of general interacting particle systems. Moreover, as the minimal port-Hamiltonian formulation is closed we identify the ports of the subsystems which admit generalized mass-spring-damper structure modelling the binary interaction of two particles. Using the information of ports we discuss the coupling of difference species in a port-Hamiltonian preserving manner.

Citation

  • Journal: Multiscale Modeling & Simulation
  • Year: 2024
  • Volume: 22
  • Issue: 4
  • Pages: 1247–1266
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
  • DOI: 10.1137/23m1547731

BibTeX

@article{Jacob_2024,
  title={{Port-Hamiltonian Structure of Interacting Particle Systems and Its Mean-Field Limit}},
  volume={22},
  ISSN={1540-3467},
  DOI={10.1137/23m1547731},
  number={4},
  journal={Multiscale Modeling & Simulation},
  publisher={Society for Industrial & Applied Mathematics (SIAM)},
  author={Jacob, Birgit and Totzeck, Claudia},
  year={2024},
  pages={1247--1266}
}

Download the bib file

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