Abstract
This paper studies simple three-layer digital dynamical systems related to recurrent-type neural networks. The input to hidden layers construct an elementary cellular automaton and the hidden to output layers are one-to-one connection described by a permutation. Depending on the permutation, the systems generate various periodic orbits. Applications include walking robots, switching power converters, and reservoir computing. In order to analyze the dynamics, we introduce two feature quantities that evaluate complexity and stability of the periodic orbits. Calculating the feature quantities in simple example systems, we have clarified that the systems can generate various stable periodic orbits. Presenting an FPGA based hardware prototype, typical periodic orbits are confirmed experimentally.
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Okano, T., Saito, T. (2023). Permutation Elementary Cellular Automata: Analysis and Application of Simple Examples. In: Tanveer, M., Agarwal, S., Ozawa, S., Ekbal, A., Jatowt, A. (eds) Neural Information Processing. ICONIP 2022. Lecture Notes in Computer Science, vol 13623. Springer, Cham. https://doi.org/10.1007/978-3-031-30105-6_27
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DOI: https://doi.org/10.1007/978-3-031-30105-6_27
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