Saddle-Node bifurcations in classical and memristive circuits

García de la Vega, Ignacio and Riaza Rodríguez, Ricardo (2016). Saddle-Node bifurcations in classical and memristive circuits. "International Journal of Bifurcation and Chaos", v. 26 (n. 4); pp. 1-20. ISSN 0218-1274. https://doi.org/10.1142/S0218127416500644.

Description

Title: Saddle-Node bifurcations in classical and memristive circuits
Author/s:
  • García de la Vega, Ignacio
  • Riaza Rodríguez, Ricardo
Item Type: Article
Título de Revista/Publicación: International Journal of Bifurcation and Chaos
Date: April 2016
ISSN: 0218-1274
Volume: 26
Subjects:
Freetext Keywords: Saddle-node bifurcation, equilibrium point, differential-algebraic equation, matrix pencil, graph, circuit model, memristor
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

This paper addresses a systematic characterization of saddle-node bifurcations in nonlinear electrical and electronic circuits. Our approach is a circuit-theoretic one, meaning that the bifurcation is analyzed in terms of the devices’ characteristics and the graph-theoretic properties of the digraph underlying the circuit. The analysis is based on a reformulation of independent interest of the saddle-node theorem of Sotomayor for semiexplicit index one differential-algebraic equations (DAEs), which define the natural context to set up nonlinear circuit models. The bifurcation is addressed not only for classical circuits, but also for circuits with memristors. The presence of this device systematically leads to nonisolated equilibria, and in this context the saddle-node bifurcation is shown to yield a bifurcation of manifolds of equilibria; in cases with a single memristor, this phenomenon describes the splitting of a line of equilibria into two, with different stability properties.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM 2015-67396-PUnspecifiedUnspecifiedUnspecified
Government of SpainMTM 2010-15102UnspecifiedUnspecifiedUnspecified

More information

Item ID: 46320
DC Identifier: http://oa.upm.es/46320/
OAI Identifier: oai:oa.upm.es:46320
DOI: 10.1142/S0218127416500644
Official URL: http://www.worldscientific.com/doi/abs/10.1142/S0218127416500644
Deposited by: Memoria Investigacion
Deposited on: 21 Jun 2017 18:18
Last Modified: 21 Jun 2017 18:18
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