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Chaos and rigorous verification of horseshoes in a class of Hopfield neural networks |
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| Authors: | Zhiping Dan Wen zhi Huang Yan Huang |
| Affiliation: | 1. Institute of Intelligent Vision and Image Information, China Three Gorges University, 443002, Yichang, People’s Republic of China 2. College of Electrical Engineering and Information Technology, China Three Gorges University, 443002, Yichang, People’s Republic of China 3. School of Computer Science and Engineering, Wuhan Institute of Technology, 430073, Wuhan, People’s Republic of China 4. Department of Mathematics, Huazhong University of Science and Technology, 430074, Wuhan, People’s Republic of China |
| 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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