PORT-HAMILTONIAN STRUCTURE OF INTERACTING PARTICLE SYSTEMS AND ITS MEAN-FIELD LIMIT

被引：0

作者：

Jacob, Birgit ^{[1
]}

Totzeck, Claudia ^{[1
]}

机构：

[1] IMACM, University of Wuppertal, Wuppertal

来源：

Multiscale Modeling and Simulation | 2024年 / 22卷 / 04期

关键词：

interacting particle systems; long-time behavior; mean-field limit; port-Hamiltonian systems;

D O I：

10.1137/23M154773

中图分类号：

学科分类号：

摘要：

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 us to characterize conserved quantities, such as Casimir functions, as well as the long-time behavior 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 modeling the binary interaction of two particles. Using the information about these ports, we discuss the coupling of difference species in a port-Hamiltonian preserving manner. © by SIAM.

引用

页码：1247 / 1266

页数：19

共 40 条

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