Turning Points of Nonlinear Circuits

Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 23)


Bifurcation theory plays a key role in the qualitative analysis of dynamical systems. In nonlinear circuit theory, bifurcations of equilibria describe qualitative changes in the local phase portrait near an operating point, and are important from both an analytical and a numerical point of view. This work is focused on quadratic turning points, which, in certain circumstances, yield saddle-node bifurcations. Algebraic conditions guaranteeing the existence of this kind of points are well-known in the context of explicit ordinary differential equations (ODEs). We transfer these conditions to semiexplicit differential-algebraic equations (DAEs), in order to impose them to branch-oriented models of nonlinear circuits. This way, we obtain a description of the conditions characterizing these turning points in terms of the underlying circuit digraph and the devices’ characteristics.



Research supported by Project MTM2010-15102 of Ministerio de Ciencia e Innovación, Spain.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Depto. de Matemática Aplicada a las Tecnologías de la Información y las ComunicacionesEscuela Técnica Superior de Ingenieros de Telecomunicación, Universidad Politécnica de MadridMadridSpain

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