Approximation and decomposition of attractors of a Hopfield neural network system
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909231017361408 |
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| author | Danca, Marius-F. Chen, Guanrong |
| author_facet | Danca, Marius-F. Chen, Guanrong |
| contents | In this paper, the Parameter Switching (PS) algorithm is used to approximate numerically attractors of a Hopfield Neural Network (HNN) system. The PS algorithm is a convergent scheme designed for approximating attractors of an autonomous nonlinear system, depending linearly on a real parameter. Aided by the PS algorithm, it is shown that every attractor of the HNN system can be expressed as a convex combination of other attractors. The HNN system can easily be written in the form of a linear parameter dependence system, to which the PS algorithm can be applied. This work suggests the possibility to use the PS algorithm as a control-like or anticontrol-like method for chaos. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07567 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation and decomposition of attractors of a Hopfield neural network system Danca, Marius-F. Chen, Guanrong Chaotic Dynamics In this paper, the Parameter Switching (PS) algorithm is used to approximate numerically attractors of a Hopfield Neural Network (HNN) system. The PS algorithm is a convergent scheme designed for approximating attractors of an autonomous nonlinear system, depending linearly on a real parameter. Aided by the PS algorithm, it is shown that every attractor of the HNN system can be expressed as a convex combination of other attractors. The HNN system can easily be written in the form of a linear parameter dependence system, to which the PS algorithm can be applied. This work suggests the possibility to use the PS algorithm as a control-like or anticontrol-like method for chaos. |
| title | Approximation and decomposition of attractors of a Hopfield neural network system |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2405.07567 |