Skip to main content
SpringerLink
Log in

Hybrid Dynamical Systems for Memristor Modelling

An Approach to Avoid the Terminal-State Problem

  • Chapter
  • First Online:
Languages, Design Methods, and Tools for Electronic System Design

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 311))

Abstract

Leon O. Chua introduced the memristor as the fourth circuit element to complete the set of fundamental passive two-terminal elements in 1971. For a long time it seemed as if memristors were just toys in the sandbox of network theorists. The situation abruptly changed in 2008 when scientists from HP reported on a nanoelectronic device, which showed a memristive behaviour. Main hopes for new opportunities and circuit concepts in the transition to increasingly smaller integrated circuits are going to be related to this discovery. For an examination of these possibilities by means of simulation, a large number of memristor models has been developed in recent years. A special property of the behavioural models of memristive nanoelectronic devices is the restricted range of internal state variables. A number of tricky solutions has been developed up to now to handle this problem. In this section we present a straightforward solution for this problem within the framework of hybrid dynamical systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abate A, D’Innocenzo A, Di Benedetto MD, Sastry S (2009) Understanding deadlock and livelock behaviors in hybrid control systems. Nonlinear Anal: Hybrid Syst 3(2):150–162. doi:10.1016/j.nahs.2008.12.005

    MATH  MathSciNet  Google Scholar 

  2. Åström KJ, Rundqwist L (1989) Integrator windup and how to avoid it. In: Proceedings of the American control conference 1989, pp 1693–1698

    Google Scholar 

  3. Batas D, Fiedler H (2011) A memristor SPICE implementation and a new approach for magnetic flux-controlled memristor modeling. IEEE Trans Nanotechnol 10(2):250–255. doi:10.1109/TNANO.2009.2038051

    Article  Google Scholar 

  4. Biolek Z, Biolek D, Biolova V (2009) SPICE model of memristor with nonlinear dopant drift. Radioengineering 18(2):210–214. http://radioeng.cz/fulltexts/2009/09_02_210_214.pdf

  5. Chua LO (1971) Memristor—the missing circuit element. IEEE Trans Circuit Theory 18:507–519. doi:10.1109/TCT.1971.1083337

    Article  Google Scholar 

  6. Chua LO (2003) Nonlinear circuit foundations for nanodevices. Part I: the four-element torus. Proc IEEE 91(11):1830–1859. doi:10.1109/JPROC.2003.818319

    Article  Google Scholar 

  7. Chua LO, Kang SM (1976) Memristive devices and systems. Proc IEEE 64(2):209–223. doi:10.1109/PROC.1976.10092

    Article  MathSciNet  Google Scholar 

  8. Corinto F, Ascoli A (2012) A boundary condition-based approach to the modeling of memristor nanostructures. IEEE Trans Circuits Syst I: Regul Pap 59:2713–2726. doi:10.1109/TCSI.2012.2190563

    Article  MathSciNet  Google Scholar 

  9. Corinto F, Ascoli A, Gilli M (2012) Mathematical models and circuit implementations of memristive systems. In: Proceedings of the international workshop on cellular nanoscale networks and their applications (CNNA) 2012. doi:10.1109/CNNA.2012.6331458

  10. da Costa HJB, de Assis Brito Filho F, de Araujo do Nascimento PI (2012) Memristor behavioural modeling and simulations using Verilog-AMS. In: Proceedings of the IEEE Latin American symposium on circuits and systems (LASCAS) 2012, pp 1–4. doi:10.1109/LASCAS.2012.6180334

  11. Di Ventra M, Pershin YV, Chua LO (2009) Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc IEEE 97(10):1717–1724. doi:10.1109/JPROC.2009.2021077

    Article  Google Scholar 

  12. Goebel R, Sanfelice RG, Tee AR (2012) Hybrid dynamical systems: modeling, stability, and robustness. Princeton University Press, Princeton

    Google Scholar 

  13. IEC 61691–6/IEEE Std 1076.1-2009 (2009) Behavioural languages—Part 6: VHDL analog and mixed-signal extensions, 1st edn. doi:10.1109/IEEESTD.2009.5464492

  14. Joglekar YN, Wolf SJ (2009) The elusive memristor: properties of basic electrical circuits. Eur J Phys 30(4):661. http://stacks.iop.org/0143-0807/30/i=4/a=001

  15. Kvatinsky S, Talisveyberg K, Fliter D, Friedman EG, Kolodny A, Weiser UC (2011) Verilog-A for memristor models. Technical Report 801, Center for Communication and Information Technlogies (CCIT). http://webee.technion.ac.il/people/skva/Memristor

  16. Kvatinsky S, Friedman EG, Kolodny A, Weiser UC (2013) TEAM: ThrEshold adaptive memristor model. IEEE Trans Circuits Syst I: Regul Pap 60:211–221. doi:10.1109/TCSI.2012.2215714

    Article  MathSciNet  Google Scholar 

  17. Lee EA, Seshia SA (2011) Introduction to embedded systems, A cyber-physical systems approach. Lulu.com. http://LeeSeshia.org/

  18. Lehtonen E, Laiho M (2010) CNN using memristors for neighborhood connections. In: Proceedings of the international workshop on cellular nanoscale networks and their applications (CNNA) 2010. doi:10.1109/CNNA.2010.5430304

  19. Meuffels P, Soni R (2012) Fundamental issues and problems in the realization of memristors. Preprint: arXiv:1207.7319v1 [cond-mat.mes-hall]. http://arxiv.org/pdf/1207.7319v1

  20. Niu D, Xiao Y, Xie Y (2012) Low power memristor-based ReRAM design with error correcting code. In: Proceedings of the 17th Asia and South Pacific design automation conference (ASP-DAC) 2012, pp 79–84. doi:10.1109/ASPDAC.2012.6165062

  21. Pickett MD, Strukov DB, Borghetti JL, Yang JJ, Snider GS, Stewart DR, Williams RS (2009) Switching dynamics in titanium dioxide memristive devices. J Appl Phys 106(7):074508–074508-6. doi:10.1063/1.3236506

  22. Prodromakis T, Peh BP, Papavassiliou C, Toumazou C (2011) A versatile memristor model with nonlinear dopant kinetics. IEEE Trans Electron Devices 58(9):3099–3105. doi:10.1109/TED.2011.2158004

    Article  Google Scholar 

  23. Strukov DB, Snider GS, Stewart DR, Williams RS (2008) The missing memristor found. Nature 453:80–83. doi:10.1038/nature06932

    Article  Google Scholar 

  24. Tetzlaff R, Bruening A (2012) Memristor technology in future electronic system design. In: Proceedings of the design, automation test in Europe conference and exhibition (DATE) 2012, p 592. doi:10.1109/DATE.2012.6176541

  25. Tetzlaff R, Schmidt T (2012) Memristors and memristive circuits—an overview. In: Proceedings of the IEEE international symposium on circuits and systems (ISCAS) 2012, pp 1590–1595. doi:10.1109/ISCAS.2012.6271557

  26. Valov I, Linn E, Tappertzhofen S, Schmelzer S, van den Hurk J, Lentz F, Waser R (2013) Nanobatteries in redox-based resistive switches require extension of memristor theory. Nat Commun 4: http://dx.doi.org/10.1038/ncomms2784

Download references

Acknowledgments

The work reported in this chapter was done within the project CoolEDesign that is part of the Leading-Edge Cluster “Cool Silicon” which is sponsored by the German Federal Ministry of Education and Research (BMBF) within the scope of the Leading-Edge Cluster Competition.

Author information

Authors and Affiliations

  1. Fraunhofer Institute for Integrated Circuits IIS, Design Automation Division EAS, Zeunerstraße 38, 01069, Dresden, Germany

    Joachim Haase & André Lange

Authors
  1. Joachim Haase
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. André Lange
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joachim Haase .

Editor information

Editors and Affiliations

  1. UMR 7606, LIP6, Sorbonne Universités, Paris, France

    Marie-Minerve Louërat

  2. CNRS, UMR 7606, LIP6, Sorbonne Universités, Paris, France

    Torsten Maehne

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Haase, J., Lange, A. (2015). Hybrid Dynamical Systems for Memristor Modelling. In: Louërat, MM., Maehne, T. (eds) Languages, Design Methods, and Tools for Electronic System Design. Lecture Notes in Electrical Engineering, vol 311. Springer, Cham. https://doi.org/10.1007/978-3-319-06317-1_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-06317-1_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06316-4

  • Online ISBN: 978-3-319-06317-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation