Skip to main content
SpringerLink
Log in

Switching Synchronization and Metastable States in 1D Memristive Networks

  • Chapter
  • First Online:
Handbook of Memristor Networks

  • 3025 Accesses

Abstract

One-dimensional (1D) memristive networks are the simplest type of memristive networks one can imagine. Yet, despite their morphological simplicity, such networks represent an important class of memory networks characterized by the strongest interaction among the network components. This chapter reviews several important dynamical features of 1D memristive networks composed of realistic threshold-type memristive systems. First of all, the accelerated and decelerated switching regimes of memristive systems are introduced and exemplified. Secondly, the phenomenon of switching synchronization is presented. Finally, it is shown that metastable transmission lines composed of metastable memristive circuits can be used to transfer the information from one space location to another. Here, the information transfer occurs in the form of a switching front propagating along the line resembling a kink in, say, classical \(\phi ^4\) field theory model. Importantly, such memristive kinks can also be used for information processing purposes. This chapter thus reveals the triad of memristive systems functionalities in their 1D networks: information processing, storage and transfer.

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 299.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 379.99
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

Notes

  1. 1.

    The lines can also be coupled by resistors.

References

  1. Adamatzky, A., Chua, L.: Memristor Networks. Springer, Cham (2014)

    Book  Google Scholar 

  2. Backus, J.: Can programming be liberated from the von Neumann style? A functional style and its algebra of programs. Comm. Assoc. Comp. Mach. 21, 613–641 (1978)

    MathSciNet  MATH  Google Scholar 

  3. Belova, T.I., Kudryavtsev, A.E.: Solitons and their interactions in classical field theory. Phys. Usp. 40, 359 (1997)

    Article  Google Scholar 

  4. Biolek, D., Kolka, Z., Biolková, V., Biolek, Z., Potrebić, M., Tošić, D.: Modeling and simulation of large memristive networks. Int. J. Circ. Theor. Appl. (2017)

    Google Scholar 

  5. Borghetti, J., Snider, G.S., Kuekes, P.J., Yang, J.J., Stewart, D.R., Williams, R.S.: ‘Memristive’ switches enable ‘stateful’ logic operations via material implication. Nature 464, 873–876 (2010)

    Article  Google Scholar 

  6. Büttiker, M., Harris, E.P., Landauer, R.: Thermal activation in extremely underdamped josephson-junction circuits. Phys. Rev. B 28, 1268–1275 (1983)

    Article  Google Scholar 

  7. Campbell, D.K., Schonfeld, J.F., Wingate, C.A.: Resonance structure in kink-antikink interactions in \(\varphi \)4 theory. Physica D 9, 1–32 (1983)

    Article  Google Scholar 

  8. Chua, L.O., Kang, S.M.: Memristive devices and systems. Proc. IEEE 64, 209–223 (1976)

    Article  MathSciNet  Google Scholar 

  9. Di Ventra, M., Pershin, Y.V.: The parallel approach. Nat. Phys. 9, 200 (2013)

    Article  Google Scholar 

  10. Di Ventra, M., Pershin, Y.V.: On the physical properties of memristive, memcapacitive and meminductive systems. Nanotechnology 24, 255201 (2013)

    Article  Google Scholar 

  11. Di Ventra, M., Pershin, Y.V., Chua, L.O.: Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc. IEEE 97(10), 1717–1724 (2009)

    Article  Google Scholar 

  12. Gazit, E.: The “correctly folded” state of proteins: is it a metastable state? Angew. Chem. Int. Ed. 41(2), 257–259 (2002)

    Article  Google Scholar 

  13. Hong, S., Auciello, O., Wouters, D.: Emerging Non-volatile Memories. Springer, New York (2014)

    Book  Google Scholar 

  14. Jo, S.H., Chang, T., Ebong, I., Bhadviya, B.B., Mazumder, P., Lu, W.: Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett. 10, 1297–1301 (2010)

    Article  Google Scholar 

  15. Jo, S.H., Kim, K.-H., Lu, W.: High-density crossbar arrays based on a Si memristive system. Nano Lett. 9, 870–874 (2009)

    Article  Google Scholar 

  16. Pershin, Y.V., Di Ventra, M.: Experimental demonstration of associative memory with memristive neural networks. Neural Netw. 23, 881 (2010)

    Article  Google Scholar 

  17. Pershin, Y.V., La Fontaine, S., Di Ventra, M.: Memristive model of amoeba learning. Phys. Rev. E 80, 021926 (2009)

    Article  Google Scholar 

  18. Pershin, Y.V., Traversa, F.L., Di Ventra, M.: Memcomputing with membrane memcapacitive systems. Nanotechnology 26, 225201 (2015)

    Article  Google Scholar 

  19. Pershin, Y.V., Di Ventra, M.: Memory effects in complex materials and nanoscale systems. Adv. Phys. 60, 145–227 (2011)

    Article  Google Scholar 

  20. Pershin, Y.V., Di Ventra, M.: Solving mazes with memristors: a massively-parallel approach. Phys. Rev. E 84, 046703 (2011)

    Article  Google Scholar 

  21. Pershin, Y.V., Di Ventra, M.: Neuromorphic, digital, and quantum computation with memory circuit elements. Proc. IEEE 100(6), 2071–2080 (2012)

    Article  Google Scholar 

  22. Pershin, Y.V., Di Ventra, M.: Self-organization and solution of shortest-path optimization problems with memristive networks. Phys. Rev. E 88, 013305 (2013)

    Article  Google Scholar 

  23. Pershin, Y.V., Slipko, V.A., Di Ventra, M.: Complex dynamics and scale invariance of one-dimensional memristive networks. Phys. Rev. E 87, 022116 (2013)

    Article  Google Scholar 

  24. Prezioso, M., Merrikh-Bayat, F., Hoskins, B.D., Adam, G.C., Likharev, K.K., Strukov, D.B.: Training and operation of an integrated neuromorphic network based on metal-oxide memristors. Nature 521(7550), 61–64 (2015)

    Article  Google Scholar 

  25. Rajaraman, R.: Solitons and instantons (1982)

    Google Scholar 

  26. Schindler, C., Staikov, G., Waser, R.: Electrode kinetics of CuSiO\(_2\)-based resistive switching cells: overcoming the voltage-time dilemma of electrochemical metallization memories. Appl. Phys. Lett. 94, 072109 (2009)

    Article  Google Scholar 

  27. Sheldon, F.C., Di Ventra, M.: Conducting-insulating transition in adiabatic memristive networks. Phys. Rev. E 95, 012305 (2017)

    Article  Google Scholar 

  28. Slipko, V.A., Pershin, Y.V.: Switching synchronization in one-dimensional memristive networks: an exact solution. Phys. Rev. E 96, 062213 (2017)

    Google Scholar 

  29. Slipko, V.A., Shumovskyi, M., Pershin, Y.V.: Switching synchronization in one-dimensional memristive networks. Phys. Rev. E 92, 052917 (2015)

    Article  MathSciNet  Google Scholar 

  30. Slipko, V.A., Pershin, Y.V.: Metastable memristive lines for signal transmission and information processing applications. Phys. Rev. E 95, 042213 (2017)

    Article  Google Scholar 

  31. Traversa, F.L., Bonani, F., Pershin, Y.V., Di Ventra, M.: Dynamic computing random access memory. Nanotechnology 25, 285201 (2014)

    Article  Google Scholar 

  32. Vion, D., Götz, M., Joyez, P., Esteve, D., Devoret, M.H.: Thermal activation above a dissipation barrier: switching of a small josephson junction. Phys. Rev. Lett. 77, 3435–3438 (1996)

    Article  Google Scholar 

  33. Vourkas, I., Stathis, D., Sirakoulis, G.: Massively parallel analog computing: Areadne’s thread was made of memristors. IEEE Trans. Emerg. Top. Comp. 6(1), 145–155 (2015)

    Google Scholar 

  34. Yang, J.J., Strukov, D.B., Stewart, D.R.: Memristive devices for computing. Nature Nanotech. 8(1), 13–24 (2013)

    Article  Google Scholar 

  35. Yu, S., Wu, Y., Jeyasingh, R., Kuzum, D., Philip Wong, H.-S.: An electronic synapse device based on metal oxide resistive switching memory for neuromorphic computation. IEEE Trans. Electron Dev. 58(8), 2729–2737 (2011)

    Article  Google Scholar 

Download references

Acknowledgements

We are grateful to M. Di Ventra and M. Shumovskyi for their contribution to some of original publications reviewed here.

Author information

Authors and Affiliations

  1. Institute of Physics, Opole University, 45-052, Opole, Poland

    Valeriy A. Slipko

  2. Department of Physics and Astronomy, University of South Carolina, Columbia, SC, 29208, USA

    Yuriy V. Pershin

Authors
  1. Valeriy A. Slipko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuriy V. Pershin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuriy V. Pershin .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, USA

    Leon Chua

  2. Democritus University of Thrace, Xanthi, Greece

    Georgios Ch. Sirakoulis

  3. Department of Computer Science and Creative Technologies, University of the West of England, Bristol, UK

    Andrew Adamatzky

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Slipko, V.A., Pershin, Y.V. (2019). Switching Synchronization and Metastable States in 1D Memristive Networks. In: Chua, L., Sirakoulis, G., Adamatzky, A. (eds) Handbook of Memristor Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-76375-0_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-76375-0_33

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-76374-3

  • Online ISBN: 978-3-319-76375-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation