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Electrical network theory of countable graphs

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1 Author(s)
Larsen, J.C. ; Math. Inst., Tech. Univ., Lyngby, Denmark

The purpose of this dissertation is to derive the equations governing electrical networks of countable graphs and to give conditions assuring that these are gradient dynamical systems on semi-Riemannian Hilbert manifolds. Furthermore, we show how symmetries in the graph give rise to a G-action on the manifold of states. Finally, we present some mathematical results about gradient dynamical systems on semi-Riemannian Banach manifolds

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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:44 ,  Issue: 11 )