Abstract
One of the key features of Cellular Neural Networks (CNN) is the ability to perform high speed computation with memory storage localized to each cell. In this work we shall present a special class of hysteresis CNN with memristor synapses operating on the edge of chaos. In general, a spatially continuous or discrete medium made of identical cells interacting with all cells located within a neighborhood exhibits complexity if the homogeneous medium can give rise to a non-homogeneous state or spatio-temporal pattern under some homogeneous initial and boundary conditions. Throughout extensive simulations we shall present non-uniform spatial-pattern generation and we shall study the global motion of excitable waves.
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References
Asai, T.: Reaction-Diffusion Media with Excitable Oregonators Coupled by Memristors. In: Networks, M. (ed.) Andrew Adamatzky, pp. 625–636. Springer, Leon Chua (2014)
Chua, L.O.: Memristor-the missing circuit element. IEEE Trans. Circuit Theory CT 18, 507–519 (1971)
Chua, L.O., Yang, L.: Cellular neural network: theory and applications. IEEE Trans. CAS. 35, 1257 (1988)
Chua, L.O: Local Activity is the origin of complexity. Int. J. Bifurcation and Chaos 15(11), 3435–3456 (2005)
Hanggi, M., Moschytz, G.: Cellular Neural Networks: Analysis. In: Design and Optimization. Kluwer Academic Publishers Pub. (2000)
Mainzer, K., Chua, L.O.: Local Activity Principle: The Cause of Complexity and Symmetry Breaking. Imperial College Press, London (2013)
Manganaro, G., Arena, P., Fortuna, L.: Cellular Neural Networks: Chaos. In: Complexity and VLSI Processing. Springer Verlag (1999)
Murray, J.D.: Mathematical Biology, 2nd edn. Springer-Verlag, Berlin (1993)
Slavova, A.: Cellular Neural Networks: Dynamics and Modeling, p. 220. Kluwer Academic Publishers (2003)
Slavova, A., Tetzlaff, R., Zafirova, Z.: Edge of chaos in nanoscale memristor CNN. In: IEEE Proceedings of ISCAS 2019 (2019)
Slavova, A.: Dynamics of a new hysteresis memristor CNN. In: IEEE Proceedings of ECCTD 2020 (2020)
Slavova, A., Tetzlaff, R.: Mathematical Analysis of Memristor CNN. ItechOpen (2019). https://doi.org/10.5772/intechopen.86446
Slavova, A., Tetzlaff, R.: Edge of chaos in reaction diffusion CNN model. Open Math. 15(1) (2017). https://doi.org/10.1515/math-2017-0002
Vidyasagar, M.: Nonlinear systems analysis, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia (2002)
Visintin, A.: Models of Hysteresis. Springer (1993)
Acknowledgment
The first author acknowledges as well the provided access to the e-infrastructure of the Centre for Advanced Computing and Data Processing, with the financial support by the Grant No BG05M2OP001-1.001-0003, financed by the Science and Education for Smart Growth Operational Program (2014-2020) and co-financed by the European Union through the European structural and Investment funds.
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Slavova, A., Tetzlaff, R. (2023). Memory Computing on the Edge of Chaos. In: Georgiev, I., Kostadinov, H., Lilkova, E. (eds) Advanced Computing in Industrial Mathematics. BGSIAM 2020. Studies in Computational Intelligence, vol 1076. Springer, Cham. https://doi.org/10.1007/978-3-031-20951-2_13
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DOI: https://doi.org/10.1007/978-3-031-20951-2_13
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