References
93
and electric-field driven ionic migration at the base of their operation, can generate
complex nonlinear dynamical evolution of their resistance that can be exploited to
build nanoscale oscillators potentially described by low-order mathematical/circuit
models. Networks of interconnected and interacting oscillators can develop
cooperative and collective dynamics, e.g., phase synchronization and other selforganizing spatiotemporal phenomena for alternative computing schemes that
overpass the limits of conventional digital and Boolean computation. Various classes
of memristor-based relaxation oscillators displaying a tunable range of periodic and
chaotic self-oscillations have been implemented in recent years. This book presents
in Chap. 5 a new method, named Flux-Charge Analysis Method (FCAM), to study
a wide class of nonlinear circuits containing ideal memristors in the flux-charge
domain. FCAM gives a clear picture of the global dynamics and the main peculiar
dynamic aspects, such as the presence of invariant manifolds, the coexistence of
different dynamics for the same set of (fixed) circuit parameters, and the new
interesting phenomenon of bifurcations without parameters, i.e., bifurcations due
to changing the initial conditions for the state variables for a fixed set of circuit
parameters.
References
1. L.O. Chua, S.M. Kang, Memristive devices and systems. Proc. IEEE 64(2), 209–223 (1976)
2. L.O. Chua, Memristor-The missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–
519 (1971)
3. L. Chua, Introduction to memristors. IEEE, New York (2009). https://ieeexplore.ieee.org/xpl/
articleDetails.jsp?arnumber=EDP091&contentType=Education+%26+Learning
4. L. Chua, Everything you wish to know about memristors but are afraid to ask. Radioengineering 24(2), 319–368 (2015)
5. L. Chua, Resistance switching memories are memristors. Appl. Phys. A 102(4), 765–783
(2011)
6. L. Chua, Five non-volatile memristor enigmas solved. Appl. Phys. A 124(8), 563 (2018)
7. L.O. Chua, C.A. Desoer, E.S. Kuh, Linear and Nonlinear Circuits (McGraw-Hill, New York,
1987)
8. L.O. Chua, Nonlinear circuit foundations for nanodevices. I. The four-element torus. Proc.
IEEE 91(11), 1830–1859 (2003)
9. D. Biolek, Z. Biolek, V. Biolkova, Pinched hysteretic loops of ideal memristors, memcapacitors and meminductors must be ‘self-crossing’. Electron. Lett. 47(25), 1385–1387 (2011)
10. H. Kim, M. Sah, C. Yang, T. Roska, L.O. Chua, Memristor bridge synapses. Proc. IEEE
100(6), 2061–2070 (2012)
11. M. Sah, H. Kim, L.O. Chua, Brains are made of memristors. IEEE Circuits Syst. Mag. 14(1),
12–36 (2014)
12. D. Ielmini, Brain-inspired computing with resistive switching memory (RRAM): devices,
synapses and neural networks. Microelectron. Eng. 190, 44–53 (2018)
13. M. Vidyasagar, Nonlinear Systems Analysis, vol. 42 (SIAM, Philadelphia, 2002)
14. J.C. Willems, Dissipative dynamical systems part I: general theory. Arch. Ration. Mech. Anal.
45(5), 321–351 (1972)
15. J.C. Willems, Dissipative dynamical systems part II: linear systems with quadratic supply
rates. Arch. Ration. Mech. Anal. 45(5), 352–393 (1972)
93
and electric-field driven ionic migration at the base of their operation, can generate
complex nonlinear dynamical evolution of their resistance that can be exploited to
build nanoscale oscillators potentially described by low-order mathematical/circuit
models. Networks of interconnected and interacting oscillators can develop
cooperative and collective dynamics, e.g., phase synchronization and other selforganizing spatiotemporal phenomena for alternative computing schemes that
overpass the limits of conventional digital and Boolean computation. Various classes
of memristor-based relaxation oscillators displaying a tunable range of periodic and
chaotic self-oscillations have been implemented in recent years. This book presents
in Chap. 5 a new method, named Flux-Charge Analysis Method (FCAM), to study
a wide class of nonlinear circuits containing ideal memristors in the flux-charge
domain. FCAM gives a clear picture of the global dynamics and the main peculiar
dynamic aspects, such as the presence of invariant manifolds, the coexistence of
different dynamics for the same set of (fixed) circuit parameters, and the new
interesting phenomenon of bifurcations without parameters, i.e., bifurcations due
to changing the initial conditions for the state variables for a fixed set of circuit
parameters.
References
1. L.O. Chua, S.M. Kang, Memristive devices and systems. Proc. IEEE 64(2), 209–223 (1976)
2. L.O. Chua, Memristor-The missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–
519 (1971)
3. L. Chua, Introduction to memristors. IEEE, New York (2009). https://ieeexplore.ieee.org/xpl/
articleDetails.jsp?arnumber=EDP091&contentType=Education+%26+Learning
4. L. Chua, Everything you wish to know about memristors but are afraid to ask. Radioengineering 24(2), 319–368 (2015)
5. L. Chua, Resistance switching memories are memristors. Appl. Phys. A 102(4), 765–783
(2011)
6. L. Chua, Five non-volatile memristor enigmas solved. Appl. Phys. A 124(8), 563 (2018)
7. L.O. Chua, C.A. Desoer, E.S. Kuh, Linear and Nonlinear Circuits (McGraw-Hill, New York,
1987)
8. L.O. Chua, Nonlinear circuit foundations for nanodevices. I. The four-element torus. Proc.
IEEE 91(11), 1830–1859 (2003)
9. D. Biolek, Z. Biolek, V. Biolkova, Pinched hysteretic loops of ideal memristors, memcapacitors and meminductors must be ‘self-crossing’. Electron. Lett. 47(25), 1385–1387 (2011)
10. H. Kim, M. Sah, C. Yang, T. Roska, L.O. Chua, Memristor bridge synapses. Proc. IEEE
100(6), 2061–2070 (2012)
11. M. Sah, H. Kim, L.O. Chua, Brains are made of memristors. IEEE Circuits Syst. Mag. 14(1),
12–36 (2014)
12. D. Ielmini, Brain-inspired computing with resistive switching memory (RRAM): devices,
synapses and neural networks. Microelectron. Eng. 190, 44–53 (2018)
13. M. Vidyasagar, Nonlinear Systems Analysis, vol. 42 (SIAM, Philadelphia, 2002)
14. J.C. Willems, Dissipative dynamical systems part I: general theory. Arch. Ration. Mech. Anal.
45(5), 321–351 (1972)
15. J.C. Willems, Dissipative dynamical systems part II: linear systems with quadratic supply
rates. Arch. Ration. Mech. Anal. 45(5), 352–393 (1972)