References
217
in the book we will develop further extensions of FCAM to circuits containing
nonlinear inductors and capacitors and higher-order elements as memcapacitors and
meminductors (Chap. 11). We will also study the application of FCAM to circuits
containing piecewise-linear approximations of nonlinear resistors (Chap. 10).
In circuit theory, conservation of flux and charge is traditionally used to analyze
the possible discontinuities of state variables due to the opening or closing of ideal
switches, or the application of impulsive (delta of Dirac) sources, in RLC circuits.
In particular, the paper [13] has developed a systematic procedure for finding
consistent initial conditions after switching, or the application of impulsive sources,
in RLC circuits. This is based on finding equivalent circuits for the elements via
incremental flux and charge at the terminals that hold in the interval (0 − , 0 + ), where
t 0 = 0 is the critical instant. The method FCAM developed in the chapter has some
relationships with the approach in [13] but also some fundamental differences. In
fact, FCAM has been conceived for application to circuits containing memristors,
and mem-elements in general, a situation where the fundamental advantages of the
analysis in the (ϕ, q)-domain show themselves at their fullest extent. Moreover,
FCAM is devoted to study the whole dynamics of memristor circuits starting from
an initial instant t 0 , not only the behavior at a certain instant.
References
1. F. Corinto, M. Forti, Memristor circuits: flux–charge analysis method. IEEE Trans. Circuits
Syst. I Regul. Pap. 63(11), 1997–2009 (2016)
2. F. Corinto, M. Forti, Memristor circuits: bifurcations without parameters. IEEE Trans. Circuits
Syst. I Regul. Pap. 64(6), 1540–1551 (2017)
3. F. Corinto, M. Forti, Memristor circuits: pulse programming via invariant manifolds. IEEE
Trans. Circuits Syst. I Regul. Pap. 65(4), 1327–1339 (2018)
4. L.O. Chua, Nonlinear circuit foundations for nanodevices. I. The four-element torus. Proc.
IEEE 91(11), 1830–1859 (2003)
5. M. Mansfield, C. O’sullivan, Understanding Physics (Wiley, Hoboken, 2011)
6. F. Corinto, P.P. Civalleri, L.O. Chua, A theoretical approach to memristor devices. IEEE J.
Emerg. Sel. Top. Circuits Syst. 5(2), 123–132 (2015)
7. L.O. Chua, Introduction to Nonlinear Network Theory (McGraw-Hill, New York, 1969)
8. L.O. Chua, C.A. Desoer, E.S. Kuh, Linear and Nonlinear Circuits (McGraw-Hill, New York,
1987)
9. P.W. Tuinenga, SPICE: A Guide to Circuit Simulation and Analysis Using PSpice, vol. 2
(Prentice Hall, Englewood Cliffs, 1995)
10. R. Riaza, DAEs in circuit modelling: a survey, in Surveys in Differential-Algebraic Equations
I (Springer, Berlin, 2013), pp. 97–136
11. M. Itoh, L.O. Chua, Memristor oscillators. Int. J. Bifurc. Chaos 18(11), 3183–3206 (2008)
12. M. Hasler, State equations for active circuits with memristors, in Chaos, CNN, Memristors and
Beyond: A Festschrift for Leon Chua (World Scientific, Singapore, 2013), pp. 518–528
13. A. Opal, J. Vlach, Consistent initial conditions of nonlinear networks with switches. IEEE
Trans. Circuits Syst. 38(7), 698–710 (1991)
217
in the book we will develop further extensions of FCAM to circuits containing
nonlinear inductors and capacitors and higher-order elements as memcapacitors and
meminductors (Chap. 11). We will also study the application of FCAM to circuits
containing piecewise-linear approximations of nonlinear resistors (Chap. 10).
In circuit theory, conservation of flux and charge is traditionally used to analyze
the possible discontinuities of state variables due to the opening or closing of ideal
switches, or the application of impulsive (delta of Dirac) sources, in RLC circuits.
In particular, the paper [13] has developed a systematic procedure for finding
consistent initial conditions after switching, or the application of impulsive sources,
in RLC circuits. This is based on finding equivalent circuits for the elements via
incremental flux and charge at the terminals that hold in the interval (0 − , 0 + ), where
t 0 = 0 is the critical instant. The method FCAM developed in the chapter has some
relationships with the approach in [13] but also some fundamental differences. In
fact, FCAM has been conceived for application to circuits containing memristors,
and mem-elements in general, a situation where the fundamental advantages of the
analysis in the (ϕ, q)-domain show themselves at their fullest extent. Moreover,
FCAM is devoted to study the whole dynamics of memristor circuits starting from
an initial instant t 0 , not only the behavior at a certain instant.
References
1. F. Corinto, M. Forti, Memristor circuits: flux–charge analysis method. IEEE Trans. Circuits
Syst. I Regul. Pap. 63(11), 1997–2009 (2016)
2. F. Corinto, M. Forti, Memristor circuits: bifurcations without parameters. IEEE Trans. Circuits
Syst. I Regul. Pap. 64(6), 1540–1551 (2017)
3. F. Corinto, M. Forti, Memristor circuits: pulse programming via invariant manifolds. IEEE
Trans. Circuits Syst. I Regul. Pap. 65(4), 1327–1339 (2018)
4. L.O. Chua, Nonlinear circuit foundations for nanodevices. I. The four-element torus. Proc.
IEEE 91(11), 1830–1859 (2003)
5. M. Mansfield, C. O’sullivan, Understanding Physics (Wiley, Hoboken, 2011)
6. F. Corinto, P.P. Civalleri, L.O. Chua, A theoretical approach to memristor devices. IEEE J.
Emerg. Sel. Top. Circuits Syst. 5(2), 123–132 (2015)
7. L.O. Chua, Introduction to Nonlinear Network Theory (McGraw-Hill, New York, 1969)
8. L.O. Chua, C.A. Desoer, E.S. Kuh, Linear and Nonlinear Circuits (McGraw-Hill, New York,
1987)
9. P.W. Tuinenga, SPICE: A Guide to Circuit Simulation and Analysis Using PSpice, vol. 2
(Prentice Hall, Englewood Cliffs, 1995)
10. R. Riaza, DAEs in circuit modelling: a survey, in Surveys in Differential-Algebraic Equations
I (Springer, Berlin, 2013), pp. 97–136
11. M. Itoh, L.O. Chua, Memristor oscillators. Int. J. Bifurc. Chaos 18(11), 3183–3206 (2008)
12. M. Hasler, State equations for active circuits with memristors, in Chaos, CNN, Memristors and
Beyond: A Festschrift for Leon Chua (World Scientific, Singapore, 2013), pp. 518–528
13. A. Opal, J. Vlach, Consistent initial conditions of nonlinear networks with switches. IEEE
Trans. Circuits Syst. 38(7), 698–710 (1991)