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Fractal variation of attractors in complex-valued neural networks

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Abstract

Fractal variation of dynamical attractors is observed in complex-valued neural networks where a negative-resistance nonlinearity is introduced as the neuron nonlinear function. When a parameter of the negative-resistance nonlinearity is continuously changed, it is found that the network attractors present a kind of fractal variation in a certain parameter range between deterministic and non-deterministic attractor ranges. The fractal pattern has a convergence point, which is also a critical point where deterministic attractors change into chaotic attractors. This result suggests that the complex-valued neural networks having negative-resistance nonlinearity present the dynamics complexity at the so-called edge of chaos.

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Authors and Affiliations

  1. Institute for Neuroinformatics (Dept. Computer Science VI), University of Bonn, Roemerstrasse 164, D-53117, Bonn, Germany

    Akira Hirose

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  1. Akira Hirose
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The author is also with the Research Center for Advanced Science and Technology (RCAST), University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153, Japan

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Hirose, A. Fractal variation of attractors in complex-valued neural networks. Neural Process Lett 1, 6–8 (1994). https://doi.org/10.1007/BF02312393

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  • DOI: https://doi.org/10.1007/BF02312393

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