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Chaos and rigorous verification of horseshoes in a class of Hopfield neural networks

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Abstract

In this paper, chaos in a new class of three-dimensional continuous time Hopfield neural networks is investigated. Numerical experiments show that this class of Hopfield neural networks can have chaotic attractors and limit cycles for different parameter configurations. By virtue of horseshoes theory in dynamic systems, rigorous computer-assisted verifications are done for their chaotic behavior. In terms of topological entropy, quantitative interpretations of these neural networks’ complexity are given. A brief analysis is also presented about their robustness.

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Acknowledgments

The research was funded by National Science Foundation of China (60875009) and the great project of Hubei Provincial Department of Education (Z20081301). The authors are very grateful to the reviewer for the valuable comments and suggestions.

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Authors and Affiliations

  1. Institute of Intelligent Vision and Image Information, China Three Gorges University, 443002, Yichang, People’s Republic of China

    Zhiping Dan

  2. College of Electrical Engineering and Information Technology, China Three Gorges University, 443002, Yichang, People’s Republic of China

    Zhiping Dan

  3. School of Computer Science and Engineering, Wuhan Institute of Technology, 430073, Wuhan, People’s Republic of China

    Wen zhi Huang

  4. Department of Mathematics, Huazhong University of Science and Technology, 430074, Wuhan, People’s Republic of China

    Yan Huang

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  1. Zhiping Dan
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Correspondence to Zhiping Dan.

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Dan, Z., Huang, W.z. & Huang, Y. Chaos and rigorous verification of horseshoes in a class of Hopfield neural networks. Neural Comput & Applic 19, 159–166 (2010). https://doi.org/10.1007/s00521-009-0269-8

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