2011/07/11 by Arjan van der Schaft, van der Schaft, A. J., Bernhard Maschke +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #Complex Network Analysis Techniques #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Gene Regulatory Network Analysis #Optimization and Control (math.OC) #Symplectic Geometry (math.SG) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1107.2006
openalex publication_date 2011/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. Basic idea is to associate with the incidence matrix of the graph a Dirac structure relating the flow and effort variables associated to the edges, internal vertices, as well as boundary vertices of the graph, and to formulate energy-storing or energy-dissipating relations between the flow and effort variables of the edges and internal vertices. This allows for state variables associated to the edges, and formalizes the interconnection of networks. Examples from different origins such as consensus algorithms are shown to share the same structure. It is shown how the identified Hamiltonian structure offers systematic tools for the analysis of the resulting dynamics.