Kolloquium: Birgit Jacob (Bergische Universität Wuppertal): Port-Hamiltonian approach to interacting particle systems

Port-Hamiltonian approach to interacting particle systems – Vortragende: Birgit Jacob, Bergische Universität Wuppertal – Einladender: M. Gugat

Port-Hamiltonian systems represent an important and attractive novel paradigm for the mathematical modeling of dynamical systems. Port-Hamiltonian coupling genuinely guarantees stability of the overall system when the individual systems are stable, a feature that is lacking in other coupling approaches. We derive a 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. Futher, the port-Hamiltonian structure is preserved in the mean-field limit.