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Horseshoe chaos in a class of simple Hopfield neural networks

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  • Yuan, Quan
  • Li, Qingdu
  • Yang, Xiao-Song

Abstract

A class of new simple Hopfield neural networks is revisited. To confirm the chaotic behavior in these Hopfield neural networks demonstrated in numerical studies, we resort to Poincaré section and Poincaré map technique and present a rigorous verification of existence of horseshoe chaos by virtue of topological horseshoes theory and estimates of topological entropy in the derived Poincaré maps.

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  • Yuan, Quan & Li, Qingdu & Yang, Xiao-Song, 2009. "Horseshoe chaos in a class of simple Hopfield neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1522-1529.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:4:p:1522-1529
    DOI: 10.1016/j.chaos.2007.06.037
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    References listed on IDEAS

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    1. Chen, Yi-Chiuan, 2006. "Smale horseshoe via the anti-integrability," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 377-385.
    2. Dai, Dong & Ma, Yue & Tse, Chi K. & Ma, Xikui, 2005. "Existence of horseshoe maps in current-mode controlled buck-boost dc/dc converters," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 549-556.
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    Cited by:

    1. Marat Akhmet & Madina Tleubergenova & Zakhira Nugayeva, 2020. "Strongly Unpredictable Oscillations of Hopfield-Type Neural Networks," Mathematics, MDPI, vol. 8(10), pages 1-14, October.

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