This paper contributes to the understanding of memristor operation and its possible application fields through: (a) derivation of a complete mathematical model for the HP memristor which takes into consideration the inter-dependence between memristance, charge and flux along with the boundary and initial conditions of operation; (b) an introduction of detailed charge- and flux-controlled SPICE memristor models realizing the proposed mathematical memristor model; (c) The incorporation of the memristor model in the SPICE realization of a third-order chaotic system where a single HP memristor acts as the nonlinear part of the system. Simulation results are provided to validate the mathematical model and the synthesis and operation of the third-order chaotic system.

Keywords:

References

P. Arenaet al., Generation of n-Double Scrolls via Cellular Neural Networks 24, 241 (2006). Google Scholar
D. Batas and H. Fiedler, IEEE Trans. Nanotechnology 10, 250 (2010). Web of Science, Google Scholar
S. Benderli and T. A. Wey, Electron. Lett. 45, 377 (2009). Web of Science, Google Scholar
D. Biolek, Z. Biolek and V. Biolkova, Spice modeling of memristive, memcapacitative and meminductive systems, Proc. ECCTD 09, European Conf. Circuit Theory and Design (2009) pp. 249–252. Google Scholar
Z. Biolek, D. Biolek and V. Biolkova, Radioengin. 18, 210 (2009). Web of Science, Google Scholar
J. Chen and G. Lü, Int. J. Bifurcation and Chaos 16, (2006). Google Scholar
L. Chenet al., Appl. Phys. Lett. 94, 162112/1 (2009). Google Scholar
H. Choiet al., Nanotechnol. 20, 345201-1 (2009). Web of Science, Google Scholar
L. O. Chua, IEEE Trans. Circuit Th. 18, 507 (1971). Google Scholar
L. O. Chua and S. M. Kang, Proc. IEEE 63, 209 (1976). Google Scholar
T. Driscollet al., Appl. Phys. Lett. 95, 043503/1 (2009). Google Scholar
T. Driscollet al., Science 325, 1518 (2009). Web of Science, Google Scholar
S. Duan and X. Liao, Phys. Lett. A 369, 37 (2007). Web of Science, Google Scholar
N. Gergel-Hackettet al., IEEE Electr. Dev. Lett. 30, 706 (2009). Web of Science, Google Scholar
X. F. Huet al., Sci. China Ser. F-Inf. Sci. 55, 461 (2012). Web of Science, Google Scholar
M. Itoh and L. O. Chua, Electron. Lett. 18, 3183 (2008). Google Scholar
S. H. Jo, K.-H. Kim and W. Lu, Nano Lett. 9, 870 (2009). Web of Science, Google Scholar
C. Li, M. Wei and J. Yu, Chaos generator based on a PWL memristor, Int. Conf. Commun. Circuits and Syst. 2009. ICCCAS 2009 (2009) pp. 944–947. Google Scholar
Z. Lin and H. Wang, Image encryption based on chaos with PWL memristor in Chua's circuit, Int. Conf. Commun. Circuits and Syst. 2009. ICCCAS 2009 (2009) pp. 964–968. Google Scholar
S. Liu, N. Wu and A. Ignatiev, Appl. Phys. Lett. 76, 2749 (2000). Web of Science, Google Scholar
B. Muthuswamy and P. Kokate, IETE 26, 417 (2009). Web of Science, Google Scholar
K. Okaet al., J. Am. Chem. Soc. 131, 3434 (2009). Web of Science, Google Scholar
Y. V. Pershin and M. Di. Ventra, Phys. Rev. B 78, 113309-1 (2008). Web of Science, Google Scholar
Y. V. Pershin and M. Di. Ventra, Phys. Rev. B 79, 153307-1 (2009). Web of Science, Google Scholar
Y. V. Pershin, S. La Fontaine and M. Di. Ventra, Phys. Rev. E 80, 021926 (2009). Web of Science, Google Scholar
G. S. Rose and M. R. Stan Jr., IEEE Trans. Circ. Syst. 54, 2380 (2007). Web of Science, Google Scholar
M. J. Sharifi and Y. M. I. Banadaki, J. Circuits Syst. Comput. 19, 407 (2010). Link, Web of Science, Google Scholar
S. Shin, K. Kim and S. Kang, IEEE Trans. Computer-Aided Des. Integr. Circuits Syst. 29, 590 (2010). Web of Science, Google Scholar
D. Stewartet al., Nano Lett. 4, 133 (2004). Web of Science, Google Scholar
D. B. Strukovet al., Nature 453, 80 (2008). Web of Science, Google Scholar
D. B. Strukov and R. S. Williams, Phys. A — Mater. Sci. Process. 94, 515 (2009). Web of Science, Google Scholar
W. Sun, C. Li and J. Yu, A simple memristor based chaotic oscillator, Int. Conf. Commun. Circuits and Syst. 2009. ICCCAS 2009 (2009) pp. 952–954. Google Scholar
J. A. K. Suykens and J. Vandewalle, IEEE Trans. Circuits and Syst.-I: Fund. Th. Appl. 40, 861 (1993). Web of Science, Google Scholar
K. S. Tanget al., IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 48, 1369 (2001). Web of Science, Google Scholar
M. Di. Ventra, Y. V. Pershin and L. O. Chua, Proc. IEEE 97, 1717 (2009). Web of Science, Google Scholar
L. Wang and X. Yang, Electron. Lett. 42, 1439 (2006). Web of Science, Google Scholar
D. Wang, H. Zhao and J. Yu, Chaos in memristor based Murali–Lakshmanan–Chua circuit, Int. Conf. Commun. Circuits and Syst. 2009. ICCCAS 200926 (2009) pp. 958–4960. Google Scholar
X. Wanget al., IEEE Electr. Dev. Lett. 30, 294 (2009). Web of Science, Google Scholar
M. E. Yalcinet al., Int. J. Bifurcation and Chaos 12, (2002). Google Scholar
Yalcin, M. E. [2004] "Cellular neural networks, multi-scroll chaos and synchronization: Theory, applications and implementations," PhD dissertation, Katholieke Universiteit Leuven, Heverlee, Belgium . Google Scholar
J. J. Yanget al., Nat. Nanotechnol. 3, 429 (2008). Web of Science, Google Scholar
X. Zhang, Z. Huang and J. Yu, IEICE Trans. Electron. E 93-C, 355 (2010). Google Scholar
G. Zhong, K. F. Man and G. Chen, Int. J. Bifurcation and Chaos 12, 2907 (2002). Link, Web of Science, Google Scholar