268
6 Memristor Circuits: Invariant Manifolds, Coexisting Attractors, Extreme. . .
References
1. H.K. Khalil, Nonlinear Systems (Prentice Hall, Englewood Cliffs, 2002)
2. L.O. Chua, Dynamic nonlinear networks: state-of-the-art. IEEE Trans. Circuits Syst. 27(11),
1059–1087 (1980)
3. T. Matsumoto, L. Chua, A. Makino, On the implications of capacitor-only cutsets and inductoronly loops in nonlinear networks. IEEE Trans. Circuits Syst. 26(10), 828–845 (1979)
4. V.I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations (Springer,
New York, 1988)
5. O. Merino, A short history of complex numbers. University of Rhode Island, Kingston (2006)
6. B. Fiedler, S. Liebscher, J.C. Alexander, Generic Hopf bifurcation from lines of equilibria
without parameters: I. Theory. J. Differ. Equ. 167(1), 16–35 (2000)
7. M. Itoh, L.O. Chua, Memristor oscillators. Int. J. Bifurc. Chaos 18(11), 3183–3206 (2008)
8. J.P. Aubin, A. Cellina, Differential Inclusions. Set-Valued Maps and Viability Theory (Springer,
Berlin, 1984)
9. A. Mees, L. Chua, The Hopf bifurcation theorem and its applications to nonlinear oscillations
in circuits and systems. IEEE Trans. Circuits Syst. 26(4), 235–254 (1979)
10. C.R. Hens, R. Banerjee, U. Feudel, S.K. Dana, How to obtain extreme multistability in coupled
dynamical systems. Phys. Rev. E 85(3), 035202 (2012)
11. M. da Cruz Scarabello, M. Messias, Bifurcations leading to nonlinear oscillations in a 3D
piecewise linear memristor oscillator. Int. J. Bifurc. Chaos 24(1), 1430001 (2014)
12. M. Messias, C. Nespoli, V.A. Botta, Hopf bifurcation from lines of equilibria without
parameters in memristor oscillators. Int. J. Bifurcation Chaos 20(2), 437–450 (2010)
13. A. Amador, E. Freire, E. Ponce, J. Ros, On discontinuous piecewise linear models for
memristor oscillators. Int. J. Bifurcation Chaos 27(6), 1730022 (2017)
14. F. Corinto, A. Ascoli, M. Gilli, Nonlinear dynamics of memristor oscillators. IEEE Trans.
Circuits Syst. I: Regul. Pap. 58(6), 1323–1336 (2011)
15. M. Gilli, F. Corinto, P. Checco, Periodic oscillations and bifurcations in cellular nonlinear
networks. IEEE Trans. Circ. Syst. I: Regul. Pap. 51(5), 948–962 (2004)
16. M. Di Marco, M. Forti, G. Innocenti, A. Tesi, Harmonic balance method to analyze bifurcations
in memristor oscillatory circuits. Int. J. Circuit Theory Appl. 46(1), 66–83 (2018)
17. G. Innocenti, M. Di Marco, M. Forti, A. Tesi, Prediction of period doubling bifurcations in
harmonically forced memristor circuits. Nonlinear Dyn. 96(2), 1169–1190 (2019)
18. B.-C. Bao, Q. Xu, H. Bao, M. Chen, Extreme multistability in a memristive circuit. Electron.
Lett. 52(12), 1008–1010 (2016)
19. A. Buscarino, C. Corradino, L. Fortuna, M. Frasca, L.O. Chua, Turing patterns in memristive
cellular nonlinear networks. IEEE Trans. Circuits Syst. I: Regul. Pap. 63(8), 1222–1230 (2016)
20. A.I. Ahamed, M. Lakshmanan, Nonsmooth bifurcations, transient hyperchaos and hyperchaotic beats in a memristive Murali–Lakshmanan–Chua circuit. Int. J. Bifurcation Chaos
23(6), 1350098 (2013)
21. V.-T. Pham, S. Vaidyanathan, C.K. Volos, S. Jafari, N.V. Kuznetsov, T.M. Hoang, A novel
memristive time-delay chaotic system without equilibrium points. Eur. Phys. J. Spec. Top.
225(1), 127–136 (2016)
22. B. Bao, Z. Ma, J. Xu, Z. Liu, Q. Xu, A simple memristor chaotic circuit with complex
dynamics. Int. J. Bifurc. Chaos 21(9), 2629–2645 (2011)
23. Q. Li, S. Hu, S. Tang, G. Zeng, Hyperchaos and horseshoe in a 4D memristive system with
a line of equilibria and its implementation. Int. J. Circuit Theory Appl. 42(11), 1172–1188
(2014)
24. R. Riaza, C. Tischendorf, Semistate models of electrical circuits including memristors. Int. J.
Circuit Theory Appl. 39(6), 607–627 (2011)
25. R. Riaza, Manifolds of equilibria and bifurcations without parameters in memristive circuits.
SIAM J. Appl. Math. 72(3), 877–896 (2012)
6 Memristor Circuits: Invariant Manifolds, Coexisting Attractors, Extreme. . .
References
1. H.K. Khalil, Nonlinear Systems (Prentice Hall, Englewood Cliffs, 2002)
2. L.O. Chua, Dynamic nonlinear networks: state-of-the-art. IEEE Trans. Circuits Syst. 27(11),
1059–1087 (1980)
3. T. Matsumoto, L. Chua, A. Makino, On the implications of capacitor-only cutsets and inductoronly loops in nonlinear networks. IEEE Trans. Circuits Syst. 26(10), 828–845 (1979)
4. V.I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations (Springer,
New York, 1988)
5. O. Merino, A short history of complex numbers. University of Rhode Island, Kingston (2006)
6. B. Fiedler, S. Liebscher, J.C. Alexander, Generic Hopf bifurcation from lines of equilibria
without parameters: I. Theory. J. Differ. Equ. 167(1), 16–35 (2000)
7. M. Itoh, L.O. Chua, Memristor oscillators. Int. J. Bifurc. Chaos 18(11), 3183–3206 (2008)
8. J.P. Aubin, A. Cellina, Differential Inclusions. Set-Valued Maps and Viability Theory (Springer,
Berlin, 1984)
9. A. Mees, L. Chua, The Hopf bifurcation theorem and its applications to nonlinear oscillations
in circuits and systems. IEEE Trans. Circuits Syst. 26(4), 235–254 (1979)
10. C.R. Hens, R. Banerjee, U. Feudel, S.K. Dana, How to obtain extreme multistability in coupled
dynamical systems. Phys. Rev. E 85(3), 035202 (2012)
11. M. da Cruz Scarabello, M. Messias, Bifurcations leading to nonlinear oscillations in a 3D
piecewise linear memristor oscillator. Int. J. Bifurc. Chaos 24(1), 1430001 (2014)
12. M. Messias, C. Nespoli, V.A. Botta, Hopf bifurcation from lines of equilibria without
parameters in memristor oscillators. Int. J. Bifurcation Chaos 20(2), 437–450 (2010)
13. A. Amador, E. Freire, E. Ponce, J. Ros, On discontinuous piecewise linear models for
memristor oscillators. Int. J. Bifurcation Chaos 27(6), 1730022 (2017)
14. F. Corinto, A. Ascoli, M. Gilli, Nonlinear dynamics of memristor oscillators. IEEE Trans.
Circuits Syst. I: Regul. Pap. 58(6), 1323–1336 (2011)
15. M. Gilli, F. Corinto, P. Checco, Periodic oscillations and bifurcations in cellular nonlinear
networks. IEEE Trans. Circ. Syst. I: Regul. Pap. 51(5), 948–962 (2004)
16. M. Di Marco, M. Forti, G. Innocenti, A. Tesi, Harmonic balance method to analyze bifurcations
in memristor oscillatory circuits. Int. J. Circuit Theory Appl. 46(1), 66–83 (2018)
17. G. Innocenti, M. Di Marco, M. Forti, A. Tesi, Prediction of period doubling bifurcations in
harmonically forced memristor circuits. Nonlinear Dyn. 96(2), 1169–1190 (2019)
18. B.-C. Bao, Q. Xu, H. Bao, M. Chen, Extreme multistability in a memristive circuit. Electron.
Lett. 52(12), 1008–1010 (2016)
19. A. Buscarino, C. Corradino, L. Fortuna, M. Frasca, L.O. Chua, Turing patterns in memristive
cellular nonlinear networks. IEEE Trans. Circuits Syst. I: Regul. Pap. 63(8), 1222–1230 (2016)
20. A.I. Ahamed, M. Lakshmanan, Nonsmooth bifurcations, transient hyperchaos and hyperchaotic beats in a memristive Murali–Lakshmanan–Chua circuit. Int. J. Bifurcation Chaos
23(6), 1350098 (2013)
21. V.-T. Pham, S. Vaidyanathan, C.K. Volos, S. Jafari, N.V. Kuznetsov, T.M. Hoang, A novel
memristive time-delay chaotic system without equilibrium points. Eur. Phys. J. Spec. Top.
225(1), 127–136 (2016)
22. B. Bao, Z. Ma, J. Xu, Z. Liu, Q. Xu, A simple memristor chaotic circuit with complex
dynamics. Int. J. Bifurc. Chaos 21(9), 2629–2645 (2011)
23. Q. Li, S. Hu, S. Tang, G. Zeng, Hyperchaos and horseshoe in a 4D memristive system with
a line of equilibria and its implementation. Int. J. Circuit Theory Appl. 42(11), 1172–1188
(2014)
24. R. Riaza, C. Tischendorf, Semistate models of electrical circuits including memristors. Int. J.
Circuit Theory Appl. 39(6), 607–627 (2011)
25. R. Riaza, Manifolds of equilibria and bifurcations without parameters in memristive circuits.
SIAM J. Appl. Math. 72(3), 877–896 (2012)