Numerically evaluated functional equivalence between chaotic dynamics in neural networks and cellular automata
under totalistic rules |
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Authors: | Ryu Takada Daigo Munetaka Shoji Kobayashi Yoshikazu Suemitsu Shigetoshi Nara |
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Institution: | (1) Department of Electronic & Information System Engineering, The Graduate School of Natural Science & Technology, Okayama University, 700-8530 Okayama, Japan;(2) Department of Electrical & Electronic Engineering, Faculty of Engineering, Okayama University, 700-8530 Okayama, Japan;(3) Kyoto School of Computer Science, Nishikujyo Minami-ku, Kyoto 601-8407, Japan;(4) Department of Electrical & Electronic Engineering, The Graduate School of Natural Science & Technology, Okayama University, 700-8530 Okayama, Japan |
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Abstract: | Chaotic dynamics in a recurrent neural network model and in two-dimensional cellular automata, where both have finite but
large degrees of freedom, are investigated from the viewpoint of harnessing chaos and are applied to motion control to indicate
that both have potential capabilities for complex function control by simple rule(s). An important point is that chaotic dynamics
generated in these two systems give us autonomous complex pattern dynamics itinerating through intermediate state points between
embedded patterns (attractors) in high-dimensional state space. An application of these chaotic dynamics to complex controlling
is proposed based on an idea that with the use of simple adaptive switching between a weakly chaotic regime and a strongly
chaotic regime, complex problems can be solved. As an actual example, a two-dimensional maze, where it should be noted that
the spatial structure of the maze is one of typical ill-posed problems, is solved with the use of chaos in both systems. Our
computer simulations show that the success rate over 300 trials is much better, at least, than that of a random number generator.
Our functional simulations indicate that both systems are almost equivalent from the viewpoint of functional aspects based
on our idea, harnessing of chaos. |
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Keywords: | Chaotic dynamics Recurrent neural network Cellular automata Information processing Complex control Adaptive function |
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