Stability breakdown along a line of equilibria in nonlinear circuits with memristors

Riaza Rodríguez, Ricardo (2015). Stability breakdown along a line of equilibria in nonlinear circuits with memristors. In: "The 2015 International Conference on Mathematical Methods, Mathematical Models and Simulation in Science and Engineering (MMSSE)", 15/03/2015 - 17/03/2015, Vienna, Austria. pp. 79-82.

Description

Title: Stability breakdown along a line of equilibria in nonlinear circuits with memristors
Author/s:
  • Riaza Rodríguez, Ricardo
Item Type: Presentation at Congress or Conference (Article)
Event Title: The 2015 International Conference on Mathematical Methods, Mathematical Models and Simulation in Science and Engineering (MMSSE)
Event Dates: 15/03/2015 - 17/03/2015
Event Location: Vienna, Austria
Title of Book: The 2015 International Conference on Mathematical Methods, Mathematical Models and Simulation in Science and Engineering (MMSSE)
Date: 2015
Subjects:
Freetext Keywords: Nonlinear circuit, memristor, equilibrium, stability, normal hyperbolicity, bifurcation
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

The design in 2008 of a device with a memristive characteristic has had a great impact in electronics, specially at the nanometer scale. This device, whose existence was predicted by Leon Chua in 1971 for symmetry reasons, is governed in a flux-controlled setting by a relation of the form i = W(ϕ)v, and systematically leads to the presence of non-isolated equilibria. In this communication we examine how the stability of such manifolds of equilibria may break down when normal hyperbolicity fails. This phenomenon may be due to the transition of an eigenvalue either through the origin or through infinity. Our approach is a graph-theoretic one, aiming at the analysis of such phenomena in terms of the topology of the digraph underlying the circuit.

More information

Item ID: 42454
DC Identifier: http://oa.upm.es/42454/
OAI Identifier: oai:oa.upm.es:42454
Official URL: http://www.inase.org/library/2015/vienna/bypaper/MAPUR/MAPUR-10.pdf
Deposited by: Memoria Investigacion
Deposited on: 17 Jul 2016 10:11
Last Modified: 17 Jul 2016 10:11
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