Abstract
We suggest and experimentally demonstrate a chaotic memory resistor (memristor). The core of our approach is to use a resistive system whose equations of motion for its internal state variables are similar to those describing a particle in a multi-well potential. Using a memristor emulator, the chaotic memristor is realized and its chaotic properties are measured. A Poincaré plot showing chaos is presented for a simple nonautonomous circuit involving only a voltage source directly connected in series to a memristor and a standard resistor. We also explore theoretically some details of this system, plotting the attractor and calculating Lyapunov exponents. The multi-well potential used resembles that of many nanoscale memristive devices, suggesting the possibility of chaotic dynamics in other existing memristive systems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Di Ventra, Y.V. Pershin, L.O. Chua, Proc. IEEE 97(10), 1717 (2009)
Y.V. Pershin, M. Di Ventra, Adv. Phys, (2010, in press). arXiv:1011.3053
L.O. Chua, IEEE Trans. Circuit Theory 18, 507 (1971)
L.O. Chua, S.M. Kang, Proc. IEEE 64, 209 (1976)
D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, Nature 453, 80 (2008)
M. Sapoff, R.M. Oppenheim, Proc. IEEE 51, 1292 (1963)
J.J. Yang, M.D. Pickett, X. Li, D.A.A. Ohlberg, D.R. Stewart, R.S. Williams, Nat. Nanotechnol. 3, 429 (2008)
S.H. Jo, K.H. Kim, W. Lu, Nano Lett. 9, 870 (2009)
N. Gergel-Hackett, B. Hamadani, B. Dunlap, J. Suehle, C. Richter, C. Hacker, D. Gundlach, IEEE Electron Device Lett. 30, 706 (2009)
T. Driscoll, H.T. Kim, B.G. Chae, M. Di Ventra, D.N. Basov, Appl. Phys. Lett. 95, 043503 (2009)
T. Driscoll, H.T. Kim, B.G. Chae, B.J. Kim, Y.W. Lee, N.M. Jokerst, S. Palit, D.R. Smith, M. Di Ventra, D.N. Basov, Science 325, 1518 (2009)
Y.V. Pershin, M. Di Ventra, Phys. Rev. B 78, 113309 (2008)
Y.V. Pershin, M. Di Ventra, Phys. Rev. B 79(15), 153307 (2009)
X. Wang, Y. Chen, Y. Gu, H. Li, IEEE Electron Device Lett. 31, 20 (2010)
P. Kuekes, D. Stewart, R. Williams, J. Appl. Phys. 97(3), 034301 (2005)
E. Lehtonen, M. Laiho, in Proceedings of the 2009 International Symposium on Nanoscale Architectures (NANOARCH’09) (2009), pp. 33–36
D.B. Strukov, R.S. Williams, Proc. Natl. Acad. Sci. USA 106, 20155 (2009)
G.S. Snider, SciDAC Rev. 10, 58 (2008)
Y.V. Pershin, S. La Fontaine, M. Di Ventra, Phys. Rev. E 80, 021926 (2009)
Y.V. Pershin, M. Di Ventra, Neural Netw. 23, 881 (2010)
T. Driscoll, J. Quinn, S. Klein, H.T. Kim, B. Kim, Y. Pershin, M. Di Ventra, D.N. Basov, Appl. Phys. Lett. 97, 093502 (2010)
B. Muthuswamy, P.P. Kokate, IETE Tech. Rev. 26, 417 (2009)
Y.V. Pershin, M. Di Ventra, IEEE Trans. Circuits Syst. I 57, 1857 (2010)
S.H. Jo, T. Chang, I. Ebong, B.B. Bhadviya, P. Mazumder, W. Lu, Nano Lett. 10, 1297 (2010)
M. Itoh, L.O. Chua, Int. J. Bifurc. Chaos 19, 3605 (2009)
D.B. Strukov, R.S. Williams, Appl. Phys. A, Mater. Sci. Process. 94, 515 (2009)
J. Martinez-Rincon, Y.V. Pershin, in preparation (2010)
M. Itoh, L.O. Chua, Int. J. Bifurc. Chaos 18, 3183 (2008)
B.C. Bao, Z. Liu, J.P. Xu, Electron. Lett. 46, 228 (2010)
B. Bao, Z. Liu, J.P. Xu, Chin. Phys. B 19, 030510 (2010)
T. Matsumoto, IEEE Trans. Circuits Syst. 31, 1055 (1984)
R.N. Madan, Chua’s Circuit: A Paradigm for Chaos (World Scientific Publishing Company, Singapore, 1993)
Y.V. Pershin, M. Di Ventra, Electron. Lett. 46, 517 (2010)
Y.V. Pershin, M. Di Ventra, arXiv:1009.6025 (2010)
M. Zwolak, D. Ferguson, M. Di Ventra, Phys. Rev. B 67, 081303 (2003)
A. Wolf, J. Swift, H. Swiney, J.A. Vastano, Physica D 16, 285 (1985)
A.R. Zeni, J.A. Gallas, Physica D 89, 71 (1995)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Driscoll, T., Pershin, Y.V., Basov, D.N. et al. Chaotic memristor. Appl. Phys. A 102, 885–889 (2011). https://doi.org/10.1007/s00339-011-6318-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00339-011-6318-z