Advertisement

Memristor Models for Pattern Recognition Systems

  • Fernando Corinto
  • Alon Ascoli
  • Marco Gilli
Part of the Springer Series in Cognitive and Neural Systems book series (SSCNS, volume 4)

Abstract

The design of Memristor Oscillatory Neurocomputers for pattern recognition tasks may not leave aside a preliminary thorough investigation of the nonlinear dynamics of the whole system and its basic components. This chapter yields novel insights into the peculiar nonlinear dynamics of different memristor models. A detailed mathematical treatment aimed at highlighting the key impact the initial condition on the flux across a memristor with odd-symmetric charge-flux characteristic has on the development of a particular dynamical behavior. It is proved how, driving the memristor with a sine-wave voltage source, the amplitude–angular frequency ratio selects a sub-class of observable current–voltage behaviors from the class of all possible dynamics, while the initial condition on flux specifies which of the behaviors in the sub-class is actually observed. In addition, a novel boundary condition-based model for memristor nano-scale films points out how specification of suitable dynamical behavior at film ends, depending on the particular physical realization under study and on driving conditions, crucially determines the observed dynamics.

Keywords

Threshold Voltage Frequency Ratio Input Amplitude Pattern Recognition System Spike Timing Dependent Plasticity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was partially supported by the CRT Foundation, under the project no. 2009.0570, by the Istituto Superiore Mario Boella and the regional government of Piedmont.

References

  1. 1.
    Mead C (1989) Analog VLSI and neural systems. Addison Wesley Longman, BostonGoogle Scholar
  2. 2.
    Boahen K (1996) Retinomorphic Vision Systems, Fifth International Conference on Microelectronics for Neural Networks and Fuzzy Systems, IEEE Computer Soc. Press, pp 2–14Google Scholar
  3. 3.
    Versace M, Chandler B (2010) MoNETA: a mind made from memristors. IEEE Spect 12:30–37Google Scholar
  4. 4.
    Dayan P, Abbott LF (2001) Theoretical neuroscience. MIT Press, CambridgeGoogle Scholar
  5. 5.
    Buzsaki G (2006) Rhythms of the brain. Oxford University Press, New YorkCrossRefGoogle Scholar
  6. 6.
    Corinto F, Ascoli A, Lanza V, Gilli M (2011) Memristor synaptic dynamics influence on synchronous behavior of two Hindmarsh-Rose neurons. Proceedings of international joint conference on neural networks, San Jose, CA, pp 2403–2408Google Scholar
  7. 7.
    Corinto F, Lanza V, Ascoli A, Gilli M (2011) Synchronization in networks of FitzHugh-Nagumo neurons with memristor synapses. Proceedings of IEEE european conference on circuit theory and design, pp 629–632Google Scholar
  8. 8.
    Engel AK, Kreiter AK, Kšnig P, Singer W (1991) Synchronization of oscillatory neuronal responses between striate and extrastriate visual cortical areas of the cat. Proc Natl Acad Sci USA 88(14):6048–6052PubMedCrossRefGoogle Scholar
  9. 9.
    Chalupa LM, Werner JS (2004) The visual neurosciences. A Bradford Book, MIT Press, CambridgeGoogle Scholar
  10. 10.
    Chua LO (1971) Memristor: the missing circuit element. IEEE Trans Circ Theor 18(5):507–519CrossRefGoogle Scholar
  11. 11.
    Strukov DB, Snider GS, Stewart DR, Williams RS (2008) The missing memristive element found. Nature 453:80–83PubMedCrossRefGoogle Scholar
  12. 12.
    Snider G, Amerson R, Carter D, Abdalla H, Qureshi MS, Léveillé J, Versace M, Ames H, Patrick S, Chandler B, Gorchetchnikov A, Mingolla E (2011) From synapses to circuitry: using memristive memory to explore the electronic brain. IEEE Comput 44(2):21–28. doi:10.1109/MC.2011.48CrossRefGoogle Scholar
  13. 13.
    Corinto F, Bonnin M, Gilli M (2007) Weakly connected oscillatory network models for associative and dynamic memories. Int J Bif Chaos 17:4365–4379CrossRefGoogle Scholar
  14. 14.
    Snider GS (2008) Spike-timing-dependent learning in memristive nanodevices. Proceedings of IEEE/ACM international symposium on nanoscale architectures, Anaheim, CA, pp 85–92Google Scholar
  15. 15.
    Pershin YV, Di Ventra M (2010) Experimental demonstration of associative memory with memristive neural networks. Neural Networks 23:881–886PubMedCrossRefGoogle Scholar
  16. 16.
    Corinto F, Ascoli A, Gilli M (2011) Nonlinear dynamics of memristor oscillators. IEEE Trans Circ Syst I 58(6):1323–1336CrossRefGoogle Scholar
  17. 17.
    Corinto F, Ascoli A, Gilli M (2010) Memristive based oscillatory associative and dynamic memories. Proceedings of international workshop on cellular nanoscale networks and Applications, Berkeley, CA, pp 1–6Google Scholar
  18. 18.
    Corinto F, Ascoli A, Gilli M (2010) Bifurcations in memristive oscillators. Proceedings workshop on nonlinear dynamics of electronic system, pp 166–169Google Scholar
  19. 19.
    Corinto F, Ascoli A, Gilli M (2011) Heteroclinic bifurcation in memristor oscillators. Proceedings of IEEE European conference on circuit theory and design, pp 237–240Google Scholar
  20. 20.
    Chua LO, Kang SM (1976) Memristive devices and systems. Proc IEEE 64(2):209–223CrossRefGoogle Scholar
  21. 21.
    Muthuswamy B (2010) Implementing memristor based chaotic circuits. Int J Bif Chaos 20(5):1335–1350CrossRefGoogle Scholar
  22. 22.
    Radwan AG, Zidan MA, Salama KN (2010) HP memristor mathematical model for periodic signals and DC. IEEE international Midwest symposium on circuits and systems, Seattle, USA, pp 861–864Google Scholar
  23. 23.
    Radwan AG, Zidan MA, Salama KN (2010) On the mathematical modeling of memristors. IEEE international conference on microelectronics, pp 284–287Google Scholar
  24. 24.
    Joglekar YN, Wolf ST (2009) The elusive memristive element: properties of basic electrical circuits. Eur J Phys 30:661–675CrossRefGoogle Scholar
  25. 25.
    Biolek Z, Biolek D, Biolková V (2009) Spice model of memristor with nonlinear dopant drift. Radioengineering 18(2):210–214Google Scholar
  26. 26.
    Corinto F, Ascoli A, Gilli M (2011) Symmetric charge–flux nonlinearity with combined inherently-asymmetric memristors. Proceedings of European conference on circuit theory and design, Linköping, Sweden, pp 653–656Google Scholar
  27. 27.
    Corinto F, Ascoli A, Gilli M (2011) Class of all i–v dynamics for memristive elements in pattern recognition systems. Proceedings of international joint conference on neural networks, pp 2289–2296Google Scholar
  28. 28.
    Corinto F, Ascoli A, Gilli M (2012) Analysis of current–voltage characteristics for memristive elements in pattern recognition systems. Int J Circ Theor Appl. doi:10.1002/cta.1804Google Scholar
  29. 29.
    Oka T, Nagaosa N (2005) Interfaces of correlated electron systems: proposed mechanism for colossal electroresistance. Phys Rev Lett 95(26):6403-1–6403-4CrossRefGoogle Scholar
  30. 30.
    Beck A, Bednorz JG, Gerber Ch, Rossel C, Widmer D (2000) Reproducible swicthing effect in thin oxide films for memory applications. Appl Phys Lett 77(1):139–141CrossRefGoogle Scholar
  31. 31.
    Linn E, Rosezin R, Kügeler C, Waser R (2010) Complementary resistive switches for passive nanocrossbar memories. Nat Mater 9:403–406PubMedCrossRefGoogle Scholar
  32. 32.
    Chua LO (2011) Resistance switching memories are memristors. Appl Phys A 102(4):765–783CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Politecnico di TorinoTorinoItaly

Personalised recommendations