Quantitative measure of hysteresis for memristors through explicit dynamics

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 468, Issue 2144, 2012, Pages 2210-2229

  Georgiou, P S ^a   Yaliraki, S N ^a   Drakakis, E M ^a   Barahona, M ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Bernoulli; Dynamics; Hysteresis; Memristor

Indexed keywords

DIFFERENTIAL EQUATIONS; DYNAMICS; HYSTERESIS; MEMRISTORS; PASSIVE FILTERS;

BERNOULLI; DESIGN AND ANALYSIS; EXPLICIT DYNAMICS; EXPLICIT FORMULA; EXPLICIT SOLUTIONS; HEWLETT-PACKARD; INPUT-OUTPUT DYNAMICS; IV CHARACTERISTICS; LUMPED PARAMETER; MATHEMATICAL FRAMEWORKS; MEMRISTOR; QUANTITATIVE MEASURES;

RESISTORS;

EID: 84864587810     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2011.0585     Document Type: Conference Paper

References (37)

1. Apostol, T. M. 1957 Mathematical analysis, 1st edn. Addison-Wesley Series in Mathematics. Reading, MA: Addison-Wesley Publishing Company.
2. Baatar, C., Porod, W. & Roska, T. 2009 Cellular nanoscale sensory wave computing, 1st edn. London, UK: Springer.
3. Borghetti, J. L., Strukov, D. B., Pickett, M. D., Yang, J. J., Stewart, D. R. & Williams, R. S. 2009 Electrical transport and thermometry of electroformed titanium dioxide memristive switches. J. Appl. Phys. 106, 124504. (doi:10.1063/1.3264621)
4. Byrd, P. F. & Friedman, M. D. 1971 Handbook of elliptic integrals for engineers and scientists, 2nd edn. Heidelberg, Germany: Springer-Verlag.
5. Cai, W., Ellinger, F., Tetzlaff, R. & Schmidt, T. 2011 Abel dynamics of titanium dioxide memristor based on nonlinear ionic drift model. (http://arxiv.org/abs/1105.2668v1).
6. Chua, L. O. 1971 Memristor: the missing circuit element. IEEE Trans. Circuit Theory 18, 507-519. (doi:10.1109/TCT.1971.1083337)
7. Chua, L. O. 1980 Device modeling via nonlinear circuit elements. IEEE Trans. Circuits Syst. 27, 1014-1044. (doi:10.1109/TCS.1980.1084742)
8. Chua, L. O. & Kang, S. M. 1976 Memristive devices and systems. Proc. IEEE. 64, 209-223. (doi:10.1109/PROC.1976.10092)
9. Drakakis, E. M. 2000 The Bernoulli cell: a transistor-level approach for log-domain filters, ch. 9. PhD thesis, Imperial College, London, UK.
10. Drakakis, E. M. & Payne, A. J. 2000 A Bernoulli cell-based investigation of the non-linear dynamics in log-domain structures. Analog. Integr. Circuits Signal Process 22, 127-146. (doi:10.1023/A:1008317708347)
11. Drakakis, E. M., Yaliraki, S. N. & Barahona, M. 2010 Memristors and Bernoulli dynamics. In Proc. of the IEEE 12th Int. Workshop on Cellular Nanoscale Networks and their Applications (CNNA), Berkeley, CA, February 2010, pp. 1-6.
12. Driscoll, T., Kim, H. T., Chae, B. G., Di'Ventra, M. & Basov, D. N. 2009 Phase-transition driven memristive system. Appl. Phys. Lett. 95, 043503. (doi:10.1063/1.3187531)
13. Georgiou, P. S., Barahona, M., Yaliraki, S. N. & Drakakis, E. M. 2011 Device properties of Bernoulli memristors. Proc. IEEE 99, 1-13. (doi:10.1109/JPROC.2011.2164889)
14. Gradshteyn, I. S. & Ryzhik, I. M. 2007 Table of integrals, series, and products, 7th edn. London, UK: Elsevier Inc.
15. Jo, S. H., Chang, T., Ebong, I., Bhadviya, B. B., Mazumder, P. & Lu, W. 2010 Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett. 10, 1297-1301. (doi:10.1021/nl904092h)
16. Joglekar, Y. N. & Wolf, S. J. 2009 The elusive memristor: properties of basic electrical circuits. Eur. J. Phys. 30, 661-675. (doi:10.1088/0143-0807/ 30/4/001)
17. Kim, T. H., Jang, E. Y., Lee, N. J., Choi, D. J., Lee, K. J., Jang, J., Choi, J.-S., Moon, H.-O. & Cheon, J. 2009 Nanoparticle assemblies as memristors. Nano Lett. 9, 2229-2233. (doi:10.1021/nl900030n)
18. Lu, J. & Chen, G. 2006 Generating multiscroll chaotic attractors: theories, methods and applications. Int. J. Bifurc. Chaos 16, 775-858. (doi:10.1142/S0218127406015179) (Pubitemid 43936686)
19. Lu, J., Chen, G., Yu, X. & Leung, H. 2004 Design and analysis of multiscroll chaotic attractors from saturated function series. IEEE Trans. Circuits Syst. I 51, 2476-2490. (doi:10.1109/TCSI.2004.838151) (Pubitemid 40009469)
20. Nedaaee Oskoee, E. & Sahimi, M. 2011 Electric currents in networks of interconnected memristors. Phys. Rev. E 83, 031105. (doi:10.1103/PhysRevE.83. 031105)
21. Oster, G. F. 1974 A note on memristors. IEEE Trans. Circuits Syst. 21, 152-152. (doi:10.1109/TCS.1974.1083778)
22. Oster, G. F. & Auslander, D. M. 1972 The memristor: a new bond graph element. J. Dyn. Syst. Meas. Control 94, 249-252. (doi:10.1115/1.3426595)
23. Perez-Carrasco, J. A., Zamarreno-Ramos, C., Serrano-Gotarredona, T. & Linares-Barranco, B. 2010 On neuromorphic spiking architectures for asynchronous STDP memristive systems. In Proc. 2010 IEEE Int. Symp. on Circuits and Systems (ISCAS), Paris, France, May 2010, pp. 1659-1662. IEEE.
24. Pershin, Y. V. & Di'Ventra, M. 2008 Spin memristive systems: spin memory effects in semiconductor spintronics. Phys. Rev. B 78, 113309. (doi:10.1103/PhysRevB.78.113309)
25. Pershin, Y. V. & Di'Ventra, M. 2011 Memory effects in complex materials and nanoscale systems. Adv. Phys. 60, 145-227. (doi:10.1080/00018732. 2010.544961)
26. Pershin, Y. V., Fontaine, S. L. & Di'Ventra, M. 2009 Memristive model of amoeba learning. Phys. Rev. E 80, 021926. (doi:10.1103/PhysRevE.80.021926)
27. Pickett, M. D., Strukov, D. B., Borghetti, J. L., Yang, J. J., Snider, G. S., Stewart, D. R. & Williams, R. S. 2009 Switching dynamics in titanium dioxide memristive devices. J. Appl. Phys. 106, 074508. (doi:10.1063/1.3236506)
28. Polyanin, A. D. & Zaitsev, V. F. 2003 Handbook of exact solutions for ordinary differential equations, 2nd edn. Boca Raton, FL: Chapman and Hall/CRC.
29. Strukov, D. B. & Williams, R. S. 2009 Exponential ionic drift: fast switching and low volatility of thin-film memristors. Appl. Phys. A 94, 515-519. (doi:10.1007/s00339-008-4975-3)
30. Strukov, D. B., Snider, G. S., Stewart, D. R. & Williams, R. S. 2008 The missing memristor found. Nature 453, 80-83. (doi:10.1038/nature06932) (Pubitemid 351630336)
31. Strukov, D. B., Borghetti, J. L. & Williams, R. S. 2009 Coupled ionic and electronic transport model of thin-film semiconductor memristive behavior. Small 5, 1058-1063. (doi:10.1002/smll.200801323)
32. Widrow, B. 1960 An adaptive ADALINE' neuron using chemical memistors', 1553-1552. Stanford Electronics Laboratories.
33. Widrow, B., Pierce, W. & Angell, J. 1961 Birth, life and death in microelectronic systems. IRE Trans. Mil. Electron. MIL-5, 191-201. (doi:10.1109/IRET-MIL.1961.5008348)
34. Williams, R. S. 2008 How we found the missing memristor. IEEE Spectrum 45, 28-35. (doi:10.1109/MSPEC.2008.4687366)
35. Xia, Q. et al. 2009 Memristor-CMOS hybrid integrated circuits for reconfigurable logic. Nano Lett. 9, 3640-3645. (doi:10.1021/nl901874j)
36. Xia, Q., Pickett, M. D., Yang, J. J., Li, X., Wu, W., Medeiros-Ribeiro, G. & Williams, R. S. 2011 Two-and three-terminal resistive switches: nanometer-scale memristors and memistors. Adv. Funct. Mater. 21, 2660-2665. (doi:10.1002/adfm.201100180)
37. Yang, J. J., Pickett, M. D., Li, X., Ohlberg, D. A. A., Stewart, D. R. & Williams, R. S. 2008 Memristive switching mechanism for metal/oxide/metal nanodevices. Nat. Nanotechnol. 3, 429-433. (doi:10.1038/nnano. 2008.160)