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Surrogating Neurons in an Associative Chaotic Neural Network

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Book cover Advances in Neural Networks – ISNN 2004 (ISNN 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3173))

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Abstract

A method of surrogate data, which is originally proposed for nonlinear time series analysis, is applied to an associative chaotic neural network in order to see which statistic of the deterministic chaos of the constituent neurons in the network for the dynamical association is important. The original associative network consists of 16 chaotic model neurons whose individuals may exhibit deterministic chaos by themselves. The associative network, whose synaptic weights are determined by a conventional auto–associative matrix of the three orthogonal patterns, shows chaotic retrievals of the stored patterns. The method of surrogation is applied to replace several neuronal sites by the surrogate data to see which statistic of the deterministic chaos of the constituent neurons is important to show the chaotic retrieval. The result shows that the auto–correlation of the time series of the output of the constituent neurons is important for maintaining the chaotic retrieval.

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References

  1. Aihara, K., Takabe, T., Toyoda, M.: Chaotic Neural Networks. Physics Letters A 144, 333–340 (1990)

    Article  MathSciNet  Google Scholar 

  2. Aihara, K.: Chaotic Neural Networks. In: Kawakami, H. (ed.) Bifurcation Phenomena in Nonlinear Systems and Theory of Dynamical Systems, pp. 143–161. World Scientific, Singapore (1990)

    Google Scholar 

  3. Adachi, M., Aihara, K.: Associative Dynamics in a Chaotic Neural Network. Neural Networks 10, 83–98 (1997)

    Article  Google Scholar 

  4. Nozawa, H.: A Neural Network Model as a Globally Coupled Map and Applications Based on Chaos. Chaos 2, 377–386 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hasegawa, M., Ikeguchi, T., Aihara, K.: Combination of Chaotic Neurodynamics with the 2-opt Algorithm to Solve Traveling Salesman Problems. Phys. Rev. Lett. 79, 2344–2347 (1997)

    Article  Google Scholar 

  6. Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., Farmer, J.D.: Testing for Nonlinearity in Time Series: The Method of Surrogate Data. Physica D 58, 77–94 (1992)

    Article  MATH  Google Scholar 

  7. e.g., Kohonen, T.: Correlation Matrix Memories. IEEE Trans. C-21, 353–359 (1972)

    Article  Google Scholar 

  8. Hopfield, J.J.: Neural Networks and Physical Systems with Emergent Collective Computation Abilities. Proceedings of National Academy of Sciences, USA 79, 2445–2558 (1982)

    Article  MathSciNet  Google Scholar 

  9. Hasegawa, M., Ikeguchi, T., Aihara, K.: An Analysis on Additive Effects on Nonlinear Dynamics for Combinatorial Optimization. The Institute of Electronics, Information and Communication Engineers – IEICE Trans. Fundamentals E80-A, 206–213 (1997)

    Google Scholar 

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Adachi, M. (2004). Surrogating Neurons in an Associative Chaotic Neural Network. In: Yin, FL., Wang, J., Guo, C. (eds) Advances in Neural Networks – ISNN 2004. ISNN 2004. Lecture Notes in Computer Science, vol 3173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28647-9_37

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  • DOI: https://doi.org/10.1007/978-3-540-28647-9_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22841-7

  • Online ISBN: 978-3-540-28647-9

  • eBook Packages: Springer Book Archive

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