Abstract
In this Chapter, a Cellular Neural/Nonlinear Network (CNN) made of memristor-based cells is introduced. The Memristive CNN consists of identical cells, each containing a memristor, an inductor and a capacitor. We show how the Memristive CNN is able to generate autowaves. We investigate then an FPGA-based implementation of it and related experimental results confirming the capabilities of the system to generate autowaves. This shows that memristor can be used not only as a fundamental block of new chaotic circuits, but also to build complex systems made of interacting memristor-based elementary cells. In such systems many complex phenomena may take place like the autowave propagation discussed in this Chapter and thus feasible hardware emulators allowing an experimental investigation of systems based on electrical analogues of memristor devices are required. In this Chapter such a platform has been realized by using an FPGA-based approach which also has the further advantage of being flexible and easily adaptable to the study of other memristor-based complex systems.
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References
Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 453, 80–83 (2008)
Tour, J.M., He, T.: The fourth element. Nature 453, 42–43 (2008)
Chua, L.O.: Memristor—the missing circuit element. IEEE Trans. Circuit Theory 18, 507–519 (1971)
Pershin, Y.V., La Fontaine, S., Di Ventra, M.: Memristive model of amoeba learning. Phys. Rev. E 80, 021926 (2009)
Driscoll, T., Quinn, J., Klein, S., Kim, H.T., Kim, B.J., Pershin, Y.V., Di Ventra, M., Basov, D.N.: Memristive adaptive filters. Appl. Phys. Lett. 97, 093502 (2010)
Shin, S., Kim, K., Kang Kang, S.M.: Memristor applications for programmable analog ICs. IEEE Trans. Nanotechnol. 410, 266–274 (2011)
Chua, L.O.: Resistance switching memories are memristors. Appl. Phys. A 102, 765–783 (2011)
Chua, L.O., Yang, L.: Cellular neural networks: applications. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 35, 1273–1290 (1988)
Chua, L.O., Yang, L.: Cellular neural networks: theory. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 35, 1257–1272 (1988)
Arena, P., Baglio, S., Fortuna, L., Manganaro, G.: Chua’s circuit can be generated by CNN cells. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 42, 123–125 (1995)
Arena, P., Baglio, S., Fortuna, L., Manganaro, G.: How state controlled CNNs generate the dynamics of the Colpitts-like oscillator. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 43, 602–605 (1996)
Perez-Munuzuri, V., Perez-Villar, V., Chua, L.O.: Autowaves for image processing on a two-dimensional CNN array of excitable nonlinear circuits: flat and wrinkled labyrinths. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 40, 174–181 (1993)
Arena, P., Baglio, S., Fortuna, L., Manganaro, G.: Self-organization in a two-layer CNN. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 45, 157–162 (1998)
Perez-Munuzuri, V., Perez-Munuzuri, V., Perez-Villar, V., Chua, L.O.: Spiral waves on a 2-D array of nonlinear circuits. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 40, 872–877 (1993)
Goras, L., Chua, L.O., Leenaerts, D.M.W.: Turing patterns in CNNs—Part I: once over lightly. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 42, 602–611 (1995)
Itoh, M., Chua, L.O.: Memristor cellular automata and memristor discrete time cellular neural networks. Int. J. Bifurc. Chaos 19, 3605–3656 (2009)
Buscarino, A., Fortuna, L., Frasca, M., Gambuzza, L.V., Sciuto, G.: Memristive chaotic circuits based on cellular nonlinear networks. Int. J. Bifurc. Chaos 22(22), 1250070–1–13 (2012)
Lehtonen, E., Laiho, M.: CNN using memristors for neighborhood connections. In: Proc. IEEE Int. Workshop Cellular Nanoscale Networks Appl. (CNNA’2010), pp. 1–4 (2010)
Chua, L.O., Roska, T.: Cellular Neural Networks and Visual Computing. Cambridge University Press, Cambridge (2002)
Chua, L.O., Hasler, M., Moschytz, G.S., Neirynck, J.: Autonomous cellular neural networks: a unified paradigm for pattern formation and active wave propagation. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 42, 559–577 (1995)
Itoh, M., Chua, L.O.: Memristor oscillator. Int. J. Bifurc. Chaos 18, 3183–3206 (2008)
Arena, P., Caponetto, R., Fortuna, L., Manganaro, G.: Cellular neural networks to explore complexity. Soft Comput. 1, 120–136 (1997)
Muthuswamy, B., Chua, L.O.: Simplest chaotic circuit. Int. J. Bifurc. Chaos 20, 1567–1580 (2010)
Kilts, S.: Advanced FPGA Design: Architecture, Implementation, and Optimization, 1st edn. Wiley/IEEE Press, New Jersey (2007)
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Pham, VT., Buscarino, A., Frasca, M., Fortuna, L. (2014). Autowaves in a Lattice of Memristor-Based Cells. In: Adamatzky, A., Chua, L. (eds) Memristor Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-02630-5_29
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DOI: https://doi.org/10.1007/978-3-319-02630-5_29
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