Reaction-Diffusion Media with Excitable Oregonators Coupled by Memristors

  • Tetsuya AsaiEmail author


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 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.


  1. 1.
    Adamatzky, A., De Lacy Costello, B., Asai, T.: Reaction-Diffusion Computers. Elsevier, London (2005)Google Scholar
  2. 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)CrossRefGoogle Scholar
  3. 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. 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)CrossRefGoogle Scholar
  5. 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)CrossRefGoogle Scholar
  6. 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)CrossRefGoogle Scholar
  7. 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. 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. 9.
    Karahaliloglu, K., Balkir, S.: Bio-inspired compact cell circuit for reaction-diffusion systems. IEEE Trans. Circ. Syst. II 52(9), 558–562 (2005)CrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 11.
    Gerhardt, M., Schuster, H., Tyson, J.J.: A cellular automaton model of excitable media. Phys. D 46, 392–415 (1990)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Adamatzky, A.: Computing in Nonlinear Media and Automata Collectives. IoP Publishing, Bristol (2001)CrossRefGoogle Scholar
  13. 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. 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)CrossRefGoogle Scholar
  15. 15.
  16. 16.
    Chua, L.O.: Memristor - the missing circuit element. IEEE Trans. Circ. Theory 18(5), 507–519 (1971)CrossRefGoogle Scholar
  17. 17.
    Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 452(1), 80–83 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Hokkaido UniversitySapporoJapan

Personalised recommendations