References
385
L
di L
dt
= v C .
Such a system is similar to that describing a planar Van der Pol oscillator (Chap. 4).
Then, we may take advantage of the theoretic results on planar Van der Pol
oscillators to study the dynamics of the considerer circuit. In particular, we can
expect that there are bifurcations without parameters when varying Φ 0 via the initial
conditions i L (t 0 ) and ϕ M (t 0 ) in the (v, i)-domain.
10.4 Discussion
This chapter has introduced a class D ext of extended memristors obtained by
interconnecting basic algebraic circuit elements given by ideal memristors and
nonlinear resistors. The proposed approach for modeling such a class is in the
spirit of classical techniques for analyzing and synthesizing nonlinear circuits. The
class D ext can be used for instance to yield a more accurate characterization and
modeling of real memristor devices with rectifying effects and complex switching
features. Finally, it has been shown that simple dynamic circuits containing extended
memristors in D ext with piecewise-linear resistors can be effectively investigated via
FCAM.
References
1. L.O. Chua, Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519
(1971)
2. D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, The missing memristor found. Nature
453(7191), 80–83 (2008)
3. S.H. Jo, T. Chang, I. Ebong, B.B. Bhadviya, P. Mazumder, W. Lu, Nanoscale memristor device
as synapse in neuromorphic systems. Nano Lett. 10(4), 1297–1301 (2010)
4. A. Ascoli, S. Slesazeck, H. Mähne, R. Tetzlaff, T. Mikolajick, Nonlinear dynamics of a locallyactive memristor. IEEE Trans. Circuits Syst. I. Regul. Pap. 62(4), 1165–1174 (2015)
5. V. Erokhin, T. Berzina, P. Camorani, A. Smerieri, D. Vavoulis, J. Feng, M.P. Fontana, Material
memristive device circuits with synaptic plasticity: learning and memory. BioNanoScience
1(1–2), 24–30 (2011)
6. S. Kumar, J.P. Strachan, R. Stanley Williams, Chaotic dynamics in nanoscale NbO 2 Mott
memristors for analogue computing. Nature 548(7667), 318 (2017)
7. L.O. Chua, S.M. Kang, Memristive devices and systems. Proc. IEEE 64(2), 209–223 (1976)
8. L. Chua, Everything you wish to know about memristors but are afraid to ask. Radioengineering 24(2), 319–368 (2015)
9. F. Corinto, P.P. Civalleri, L.O. Chua, A theoretical approach to memristor devices. IEEE J.
Emerg. Select. Top. Circuits Syst. 5(2), 123–132 (2015)
10. H.K. Khalil, Nonlinear Systems (Prentice Hall, Upper Saddle River, 2002)
11. D. Panda, P.P. Sahu, T. Y. Tseng, A collective study on modeling and simulation of resistive
random access memory. Nanoscale Res. Lett. 13(1), 8 (2018)
385
L
di L
dt
= v C .
Such a system is similar to that describing a planar Van der Pol oscillator (Chap. 4).
Then, we may take advantage of the theoretic results on planar Van der Pol
oscillators to study the dynamics of the considerer circuit. In particular, we can
expect that there are bifurcations without parameters when varying Φ 0 via the initial
conditions i L (t 0 ) and ϕ M (t 0 ) in the (v, i)-domain.
10.4 Discussion
This chapter has introduced a class D ext of extended memristors obtained by
interconnecting basic algebraic circuit elements given by ideal memristors and
nonlinear resistors. The proposed approach for modeling such a class is in the
spirit of classical techniques for analyzing and synthesizing nonlinear circuits. The
class D ext can be used for instance to yield a more accurate characterization and
modeling of real memristor devices with rectifying effects and complex switching
features. Finally, it has been shown that simple dynamic circuits containing extended
memristors in D ext with piecewise-linear resistors can be effectively investigated via
FCAM.
References
1. L.O. Chua, Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519
(1971)
2. D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, The missing memristor found. Nature
453(7191), 80–83 (2008)
3. S.H. Jo, T. Chang, I. Ebong, B.B. Bhadviya, P. Mazumder, W. Lu, Nanoscale memristor device
as synapse in neuromorphic systems. Nano Lett. 10(4), 1297–1301 (2010)
4. A. Ascoli, S. Slesazeck, H. Mähne, R. Tetzlaff, T. Mikolajick, Nonlinear dynamics of a locallyactive memristor. IEEE Trans. Circuits Syst. I. Regul. Pap. 62(4), 1165–1174 (2015)
5. V. Erokhin, T. Berzina, P. Camorani, A. Smerieri, D. Vavoulis, J. Feng, M.P. Fontana, Material
memristive device circuits with synaptic plasticity: learning and memory. BioNanoScience
1(1–2), 24–30 (2011)
6. S. Kumar, J.P. Strachan, R. Stanley Williams, Chaotic dynamics in nanoscale NbO 2 Mott
memristors for analogue computing. Nature 548(7667), 318 (2017)
7. L.O. Chua, S.M. Kang, Memristive devices and systems. Proc. IEEE 64(2), 209–223 (1976)
8. L. Chua, Everything you wish to know about memristors but are afraid to ask. Radioengineering 24(2), 319–368 (2015)
9. F. Corinto, P.P. Civalleri, L.O. Chua, A theoretical approach to memristor devices. IEEE J.
Emerg. Select. Top. Circuits Syst. 5(2), 123–132 (2015)
10. H.K. Khalil, Nonlinear Systems (Prentice Hall, Upper Saddle River, 2002)
11. D. Panda, P.P. Sahu, T. Y. Tseng, A collective study on modeling and simulation of resistive
random access memory. Nanoscale Res. Lett. 13(1), 8 (2018)