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題名: | Solution Structure of Multi-layer Neural Networks with Initial Condition | 作者: | 班榮超 Ban, Jung-Chao Chang, Chih-Hung |
貢獻者: | 應數系 | 關鍵詞: | Initial value problem ; Cellular neural networks ; Sofic shift ; Path set | 日期: | 三月-2016 | 上傳時間: | 27-五月-2020 | 摘要: | This paper studies the initial value problem of multi-layer cellular neural networks. We demonstrate that the mosaic solutions of such system is topologically conjugated to a new class in symbolic dynamical systems called the path set (Abram and Lagarias in Adv Appl Math 56:109–134, 2014). The topological entropies of the solution, output, and hidden spaces of a multi-layer cellular neural network with initial condition are formulated explicitly. Also, a sufficient condition for whether the mosaic solution space of a multi-layer cellular neural network is independent of initial conditions is addressed. Furthermore, two spaces exhibit identical topological entropy if and only if they are finitely equivalent. | 關聯: | Journal of Dynamics and Differential Equations, Vol.28, No.1, pp.69-92 | 資料類型: | article | DOI: | https://doi.org/10.1007/s10884-015-9471-9 |
Appears in Collections: | 期刊論文 |
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