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On the Mathematical Modeling of Memristor, Memcapacitor, and Meminductor

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 26))

Abstract

This chapter summarizes the basic linear circuit elements (resistor, capacitor, inductor, and fractional-order elements) with their basic fundamentals and characteristic graphs. Each element was defined by a relation between the state variables of the network: current \(I\), voltage \(V\), charge \(Q\), and flux \(\varphi \). It also investigates the basic fundamentals of the memristor, its historical background, and its advantages over the last few decades. Moreover, the organization of the book is also discussed.

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References

  1. Nilsson, J.W., Riedel, S.A.: Electric Circuits, vol. 8. Prentice Hall, Reading (2009)

    Google Scholar 

  2. Miller, K.S., Ross, B.: An introduction to the fractional integrals and derivatives-theory and applications. Gordon and Breach, Longhorne, PA (1993)

    Google Scholar 

  3. Oldham, K.B., Spanier, J.: The Fractional Calculus, vol. 1047. Academic Press, New York (1974)

    MATH  Google Scholar 

  4. Carlson, G., Halijak, C.: IEEE Trans. Circuit Theory 11(2), 210 (1964)

    Google Scholar 

  5. Krishna, B., Reddy, K.: Active and passive electronic components 2008 (2008)

    Google Scholar 

  6. Nakagawa, M., Sorimachi, K.: IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 75(12), 1814 (1992)

    Google Scholar 

  7. Roy, S.: IEEE Trans. Circuit Theory 14(3), 264 (1967)

    Google Scholar 

  8. Michio, S., Hirano, Y., Miura, Y.F., Saito, K.: IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 82(8), 1627 (1999)

    Google Scholar 

  9. Schäfer, I., Krüger, K.: J. Phys. D: Appl. Phys. 41(4), 045001 (2008)

    Google Scholar 

  10. Westerlund, S., Ekstam, L.: IEEE Trans. Dielectr. Electr. Insul. 1(5), 826 (1994)

    Google Scholar 

  11. Jesus, I.S., Machado, J., Cunha, J.B., Silva, M.F.: In: Proceedings of the 25th IASTED International Conference on Modeling, Indentification, and Control, pp. 489–494. ACTA Press (2006)

    Google Scholar 

  12. Elwakil, A., Maundy, B.: Electron. Lett. 46(20), 1367 (2010)

    Google Scholar 

  13. Sabatier, J., Agrawal, O.P., Machado, J.T.: Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, The Netherlands (2007)

    Book  Google Scholar 

  14. Ford, N.J., Simpson, A.C.: Numer. Algorithms 26(4), 333 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Diethelm, K., Ford, N.J., Freed, A.D., Luchko, Y.: Comput. Methods Appl. Mech. Eng. 194(6), 743 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  16. Magin, R.L.: Crit. Rev. Biomed. Eng. 32(1) (2004)

    Google Scholar 

  17. Magin, R.L.: Crit. Rev. Biomed. Eng. 32(2) (2004)

    Google Scholar 

  18. Magin, R.L.: Crit. Rev. Biomed. Eng. 32(3&4) (2004)

    Google Scholar 

  19. Moaddy, K., Radwan, A.G., Salama, K.N., Momani, S., Hashim, I.: Comput. Math. Appl. 64(10), 3329 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  20. Doehring, T.C., Freed, A.D., Carew, E.O., Vesely, I., et al.: J. Biomech. Eng. 127(4), 700 (2005)

    Article  Google Scholar 

  21. Faryad, M., Naqvi, Q.A.: Prog. Electromag. Res. 75, 383 (2007)

    Article  Google Scholar 

  22. Li, H., Wu, M., Wang, X.T.: Chaos Solitons Fractals 42(1), 412 (2009)

    Google Scholar 

  23. Magin, R., Ovadia, M.: J. Vib. Control 14(9–10), 1431 (2008)

    Article  MATH  Google Scholar 

  24. Radwan, A.G., Elwakil, A.S., Soliman, A.M.: IEEE Trans. Circuits Syst. I: Regul. Pap. 55(7), 2051 (2008)

    Google Scholar 

  25. Radwan, A., Soliman, A., Elwakil, A.: Int. J. Circuit Theory Appl. 36(4), 473 (2008)

    Article  MATH  Google Scholar 

  26. Radwan, A.G., Soliman, A.M., Elwakil, A.S.: J. Circuits Syst. Comput. 17(01), 55 (2008)

    Google Scholar 

  27. Radwan, A.G., Elwakil, A.S., Soliman, A.M.: J. Circuits Syst. Comput. 18(02), 361 (2009)

    Google Scholar 

  28. Soltan, A., Radwan, A.G., Soliman, A.M.: Microelectron. J. 43, 818 (2012)

    Article  Google Scholar 

  29. Petrá, I.: Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation. Springer, New York (2011)

    Book  Google Scholar 

  30. Cisse Haba, T., Loum, G.L., Zoueu, J.T., Ablart, G.: J. Appl. Sci. 8, 59 (2008)

    Google Scholar 

  31. Biswas, K., Sen, S., Dutta, P.K.: Sens. Actuators A: Phys. 120(1), 115 (2005)

    Article  Google Scholar 

  32. Jesus, I.S., Machado, J.T.: Nonlinear Dyn. 56(1–2), 45 (2009)

    Article  MATH  Google Scholar 

  33. Haba, T.C., Loum, G.L., Ablart, G.: Chaos Solitons Fractals 33(2), 364 (2007)

    Google Scholar 

  34. Cisse Haba, T., Ablart, G., Camps, T., Olivie, F.: Chaos Solitons Fractals 24(2), 479 (2005)

    Google Scholar 

  35. Memristor and memristive systems symposium. http://www.youtube.com/watch?v=QFdDPzcZwbs

  36. Chua, L.: IEEE Trans. Circuit Theory 18(5), 507 (1971)

    Google Scholar 

  37. Lin, D., Chua, L., Hui, S.Y.: Proc. IEEE 103(1), 131 (2015)

    Article  Google Scholar 

  38. Widrow, B., et al.: Adaptive “ADALINE” Neuron Using Chemical “Memistors” (1960)

    Google Scholar 

  39. Adhikari, S., Kim, H.: IEEE Trans. Circuits Syst. I: Regul. Pap. 59(11), 2611 (2012). doi:10.1109/TCSI.2012.2189057

  40. Argall, F.: Solid-State Electron. 11(5), 535 (1968)

    Article  Google Scholar 

  41. Chua, L., Kang, S.: Proc. IEEE 64(2), 209 (1976)

    Article  MathSciNet  Google Scholar 

  42. Chua, L.: IEEE Trans. Circuits Syst. 27(11), 1014 (1980)

    Google Scholar 

  43. Thakoor, S., Moopenn, A., Daud, T., Thakoor, A.: J. Appl. Phys. 67(6), 3132 (1990)

    Article  Google Scholar 

  44. Buot, F., Rajagopal, A.: J. Appl. Phys. 76(9), 5552 (1994)

    Article  Google Scholar 

  45. Beck, A., Bednorz, J., Gerber, C., Rossel, C., Widmer, D.: Appl. Phys. Lett. 77(1), 139 (2000)

    Article  Google Scholar 

  46. Strukov, D., Snider, G., Stewart, D., Williams, R.: Nature 453(7191), 80 (2008)

    Article  Google Scholar 

  47. Erokhin, V., Fontana, M.P.: (2008) arXiv preprint arXiv:0807.0333

  48. Snider, G.: Molecular-junction-nanowire-crossbar-based neural network. US Patent 7,359,888 (2008)

    Google Scholar 

  49. Williams, R.S., Strukov, D.B., Bratkovski. A.: Memristive device and methods of making and using the same. US Patent App. 13/120,905 (2008)

    Google Scholar 

  50. Stewart, D.R., Beck, P.A., Ohlberg, D.A.: Non-volatile programmable impedance nanoscale devices. US Patent 7,443,711 (2008)

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Engineering, Engineering Mathematics and Physics Department, Cairo University, Giza, Egypt

    Ahmed G. Radwan & Mohammed E. Fouda

  2. Nanoelectronics Integrated Systems Center (NISC), Nile University, Cairo, Egypt

    Ahmed G. Radwan

Authors
  1. Ahmed G. Radwan
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  2. Mohammed E. Fouda
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Correspondence to Ahmed G. Radwan .

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Radwan, A.G., Fouda, M.E. (2015). Introduction. In: On the Mathematical Modeling of Memristor, Memcapacitor, and Meminductor. Studies in Systems, Decision and Control, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-17491-4_1

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  • DOI: https://doi.org/10.1007/978-3-319-17491-4_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17490-7

  • Online ISBN: 978-3-319-17491-4

  • eBook Packages: EngineeringEngineering (R0)

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