Nonlinear circuits
Time-domain models of nonlinear circuits are often set
up using a differential-algebraic formalism. This avoids the need to
perform a state-space reduction (often unfeasible in practice) before
addressing whatever analytical aspects or doing numerical simulation.
Many
simulators set up the circuit equations in DAE form. In this context,
differential-algebraic models are often referred to as semistate
models. A detailed introduction to DAE-based circuit modelling can be
found in Chapters 5 and 6 of my book Differential-Algebraic Systems,
World Scientific, 2008.
After 2008, a considerable amount of research on
nonlinear circuit theory were directed to circuits with memristors
and other related devices.
More recently (since 2018) I have been working on a formalism based on projective geometry
for general circuit modelling. Some results in this direction can be found in the Homogeneous circuit models
section below.
Papers
Here is a list of papers on circuit modelling
and analysis and their application in Electronics, or on related topics:
Homogeneous circuit models
R. Riaza, Homogeneous models of nonlinear circuits,
IEEE Transactions on Circuits and Systems I, Vol. 67 (2020) 2002-2015. Preprint version (arXiv).
R. Riaza, Associate submersions and qualitative properties of nonlinear circuits with implicit characteristics,
International Journal of Bifurcation and Chaos, Vol. 30 (2020) 2050033. Preprint version (arXiv).
R. Riaza, Circuit theory in projective space and homogeneous circuit models,
IEEE Transactions on Circuits and Systems I, Vol. 66 (2019) 463-476. Preprint version (arXiv).
Memristors
and
memory-devices
R. Riaza, Transcritical bifurcation without parameters in memristive circuits,
SIAM Journal on Applied Mathematics, Vol. 78 (2018) 395-417.
I. García de la Vega and R. Riaza,
Saddle-node bifurcations in classical and memristive circuits,
International Journal of
Bifurcation and Chaos, Vol. 26 (2016) 1650064.
R. Riaza, Second order mem-circuits,
International Journal of Circuit Theory and
Applications, Vol. 43 (2015) 1719-1742.
R. Riaza, Comment: Is memristor a dynamic element?, Electronics Letters,
Vol. 50 (2014) 1342 - 1344.
R. Riaza, First order mem-circuits: modeling,
nonlinear oscillations and bifurcations,
IEEE Transactions on Circuits and Systems - I, Vol. 60 (2013) 1570-1583.
Pre-peer reviewed version (arXiv).
R. Riaza, Manifolds of equilibria and bifurcations
without parameters in memristive circuits, SIAM J.
Applied Mathematics, Vol. 72 (2012) 877-896.
F. García-Redondo and R. Riaza, The
tractability index of memristive circuits: branch-oriented and
tree-based models,
Mathematical Methods in the Applied Sciences, Vol. 35 (2012) 1659-1699.
R. Riaza,
Dynamical properties of electrical
circuits with fully nonlinear memristors (pre-peer
reviewed version, arXiv). Nonlinear Analysis: Real World Applications,
Vol. 12 (2011) 3674-3686.
Final version (journal website).
R. Riaza,
Explicit ODE reduction of memristive systems,
International Journal of Bifurcation and Chaos,
Vol. 21 (2011) 917-930.
R. Riaza and C. Tischendorf,
Semistate models of electrical circuits including memristors,
International Journal of Circuit Theory and
Applications, Vol. 39 (2011) 607-627. Final
version (journal website).
R. Riaza, Nondegeneracy conditions for
active memristive circuits, IEEE Transactions on
Circuits and Systems - II, Vol. 57 (2010) 223-227.
Analytical aspects of
nonlinear circuit theory
I. García de la Vega and R. Riaza, Index and solvability of uncoupled circuits: A characterization without restrictions on their passivity, topology or controlling structure,
Journal of Circuits, Systems, and Computers, Vol. 23 (2014) 1450087 (31 pages).
R. Riaza, DAEs in circuit modelling: A survey, in A. Ilchmann, T. Reis (eds.), Surveys in Differential-Algebraic Equations I, pp. 97-136, DAE Forum, Springer, 2013.
I. García de la Vega and R. Riaza, Hybrid analysis of nonlinear circuits: DAE
models with indices zero and one,
Circuits, Systems, and Signal Processing, Vol. 32 (2013) 2065-2095.
R. Riaza and C. Tischendorf, Structural
characterization of classical and memristive circuits
with purely imaginary eigenvalues,
International Journal of Circuit Theory and
Applications, Vol. 41 (2013) 273-294.
R. Riaza and C. Tischendorf, The hyperbolicity problem in electrical
circuit theory,
Mathematical Methods in the Applied Sciences, Vol.
33 (2010) 2037-2049.
Final version (journal website).
R. Riaza, Graph-theoretic characterization
of bifurcation phenomena in electrical circuit dynamics,
International Journal of Bifurcation and Chaos, Vol. 20 (2010) 451-465.
A. J. Encinas and R. Riaza, Tree-based
characterization of low index circuit configurations without passivity
restrictions, International Journal of Circuit
Theory and
Applications, Vol. 36 (2008) 135-160.
R. Riaza and C. Tischendorf, Qualitative features of matrix pencils
and DAEs arising in circuit dynamics, Dynamical
Systems, Vol.
22 (2007) 107-131.
R. Riaza, Time-domain
properties of reactive dual circuits, International
Journal of Circuit Theory and
Applications, Vol. 34 (2006) 317-340.
R. Riaza, Singularity-induced bifurcations in lumped
circuits, IEEE Transactions on Circuits and Systems
- I, Vol. 52 (2005) 1442-1450.
R. Riaza and J. Torres-Ramírez, Nonlinear
circuit modelling via nodal methods, International
Journal of Circuit Theory and
Applications, Vol. 33 (2005) 281-305.
R. Riaza, A
matrix pencil approach to the local stability analysis
of non-linear circuits, International Journal of
Circuit Theory and
Applications, Vol. 32 (2004) 23-46.
Applications of digraph
theory to circuit analysis
R. Riaza,
Cyclic matrices of weighted digraphs,
Discrete Applied Mathematics, Vol. 160 (2012) 280-290.
R. Riaza and A. J. Encinas, Augmented nodal matrices and normal trees,
Discrete Applied Mathematics, Vol. 158 (2010) 44-61.
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