Skip to main content
SpringerLink
Log in

Reaction-Diffusion Media with Excitable Oregonators Coupled by Memristors

  • Chapter
  • First Online:
Handbook of Memristor Networks

Abstract

This chapter presents dynamic behaviors of a new reaction-diffusion-type excitable medium, where the diffusion coefficient is represented by memristive dynamics. The medium consists of an array of excitable Oregonators, and each Oregonator is locally coupled with other Oregonators via memristors, which were claimed to be the fourth circuit element exhibiting a relationship between flux \(\phi \) and charge q. By using the medium, this chapter exhibits that (i) the memristor conductances are modulated by the excitable waves and controlled the velocity of the waves, depending on the memristor’s polarity, and (ii) nonuniform spatial patterns are generated depending on the initial condition of Oregonator’s state, memristor polarity and stimulation.

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

References

  1. Adamatzky, A., De Lacy Costello, B., Asai, T.: Reaction-Diffusion Computers. Elsevier, London (2005)

    Google Scholar 

  2. Adamatzky, A., Arena, P., Basile, A., Carmona-Galán, R., De Lacy Costello, B., Fortuna, L., Frasca, M., Rodríguez-Vázquez, A.: Reaction-diffusion navigation robot control: from chemical to VLSI analogic processors. IEEE Trans. Circuit Syst. I 51(5), 926–938 (2004)

    Article  Google Scholar 

  3. Asai, T., Nishimiya, Y., Amemiya, Y.: A CMOS reaction-diffusion circuit based on cellular-automaton processing emulating the Belousov-Zhabotinsky reaction. IEICE Trans. Fundamentals E85–A(9), 2093–2096 (2002)

    Google Scholar 

  4. Matsubara, Y., Asai, T., Hirose, T., Amemiya, Y.: Reaction-diffusion chip implementing excitable lattices with multiple-valued cellular automata. IEICE Electron. Express 1(9), 248–252 (2004)

    Article  Google Scholar 

  5. Rekeczky, C., Roska, T., Carmona, R., Jiménez-Garrido, F., Rodríguez-Vázquez, A.: Exploration of spatial-temporal dynamic phenomena in a 32 \(\times \) 32-cell stored program two-layer CNN universal machine chip prototype. J. Circ. Syst. Comput. 12(6), 691–710 (2003)

    Article  Google Scholar 

  6. Shi, B.E., Luo, B.T.: Spatial pattern formation via reaction-diffusion dynamics in 32 \(\times \) 32 \(\times \) 4 CNN chip. IEEE Trans. Circ. Syst. I 51(5), 939–947 (2004)

    Article  Google Scholar 

  7. Asai, T., Kanazawa, Y., Hirose, T., Amemiya, Y.: Analog reaction-diffusion chip imitating the Belousov-Zhabotinsky reaction with hardware Oregonator model. Int. J. Unconventional Comput. 1(2), 123–147 (2005)

    Google Scholar 

  8. Daikoku, T., Asai, T., Amemiya, Y.: An analog CMOS circuit implementing Turing’s reaction-diffusion model. In: Proceedings of the International Symposium on Nonlinear Theory and Its Applications, pp. 809–812 (2002)

    Google Scholar 

  9. Karahaliloglu, K., Balkir, S.: Bio-inspired compact cell circuit for reaction-diffusion systems. IEEE Trans. Circ. Syst. II 52(9), 558–562 (2005)

    Article  Google Scholar 

  10. Serrano-Gotarredona, T., Linares-Barranco, B.: Log-domain implementation of complex dynamics reaction-diffusion neural networks. IEEE Trans. Neural Networks 14(5), 1337–1355 (2003)

    Article  Google Scholar 

  11. Gerhardt, M., Schuster, H., Tyson, J.J.: A cellular automaton model of excitable media. Phys. D 46, 392–415 (1990)

    Article  MathSciNet  Google Scholar 

  12. Adamatzky, A.: Computing in Nonlinear Media and Automata Collectives. IoP Publishing, Bristol (2001)

    Book  Google Scholar 

  13. Oya, T., Asai, T., Fukui, T., Amemiya, Y.: Reaction-diffusion systems consisting of single-electron circuits. Int. J. Unconventional Comput. 1(2), 177–194 (2005)

    Google Scholar 

  14. Asai, T., Adamatzky, A., Amemiya, Y.: Towards reaction-diffusion computing devices based on minority-carrier transport in semiconductors. Chaos Solitons Fractals 20(4), 863–876 (2004)

    Article  Google Scholar 

  15. http://www.scholarpedia.org/article/Oregonator

  16. Chua, L.O.: Memristor - the missing circuit element. IEEE Trans. Circ. Theory 18(5), 507–519 (1971)

    Article  Google Scholar 

  17. Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 452(1), 80–83 (2008)

    Article  Google Scholar 

Download references

Acknowledgements

This study was supported by a Grant-in-Aid for Scientific Research on Innovative Areas [20111004] from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.

Author information

Authors and Affiliations

  1. Hokkaido University, Kita 14, Nishi 9, Kita-ku, Sapporo, Hokkaido, 060-0814, Japan

    Tetsuya Asai

Authors
  1. Tetsuya Asai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tetsuya Asai .

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

Asai, T. (2019). Reaction-Diffusion Media with Excitable Oregonators Coupled by Memristors. In: Chua, L., Sirakoulis, G., Adamatzky, A. (eds) Handbook of Memristor Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-76375-0_44

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-76375-0_44

  • 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