Horseshoe chaos in a class of simple Hopfield neural networks |
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| Authors: | Quan Yuan Qingdu Li Xiao-Song Yang |
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| Institution: | 1. The Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;2. Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China;1. Department of Computer Science and Engineering, Korea University, Seoul 136-713, Republic of Korea;2. SecurityLab Technologies, Tokyo, Japan;1. Department of Computer Science, University of Oxford, United Kingdom;2. Delft Center for Systems & Control, Delft University of Technology, The Netherlands;3. Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands |
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| 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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