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| 研究生： |
陳冠瑋 Chen, Guan-Wei |
|---|---|
| 論文名稱： |
具時間延遲之霍普菲爾神經網路的多重穩定性 Multistability in Hopfield-type neural networks with delays |
| 指導教授： |
曾睿彬
Tseng, Jui-Pin |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2017 |
| 畢業學年度： | 105 |
| 語文別： | 英文 |
| 論文頁數： | 99 |
| 中文關鍵詞： | 神經網路 、多重穩定性 、時間延遲 、收斂性 |
| 相關次數： | 點閱：40 下載：11 |
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這篇論文研究具多重穩定性之時間延遲型霍普菲爾神經網路。我們以兩個神經元所組成的神經網路來表現我們的想法。運用方程式的幾何結構，我們可推導出各種使網路具有不同數量固定點的條件，我們可以進一步建立網路系統的全局收斂性。
中文摘要 iii
Abstract iv
Contents v
List of figures vii
List of tables ix
1 Introduction 1
2 Literature review and study motivation 3
2.1 General cases 3
2.2 Other cases for n = 2 6
3 Main results 10
3.1 Exact number of equilibria for case 1 10
3.1.1 K2(p˜2; A1) > 0 10
3.1.2 K2(p˜2; C1) < 0 16
3.1.3 K2(p˜2; A1) < 0 < K2(p˜2; B1) 24
3.1.4 K2(p˜2; B1) < 0 < K2(p˜2; C1) 31
3.2 Exact number of equilibria for case 2 39
3.2.1 K2(p˜2; A1) > 0 41
3.2.2 K2(p˜2; A1) < 0 < K2(p˜2; S1) and K1(q˜1; SS1 ) > 0 51
3.2.3 K2(p˜2; S1) < 0 and K1(q˜1; AS1 ) > 0 57
3.3 Convergence of dynamics for case 1 under conditions K2(p˜2; A1) > 0 69
4 Numerical examples 78
References 98
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[2] Sue Ann Campbell, R. Edwards, and P. van den Driessche. Delayed coupling between two neural network loops. SIAM J. Appl. Math., 65(1):316–335, 2004.
[3] Chang-Yuan Cheng, Kuang-Hui Lin, Chih-Wen Shih, and Jui-Pin Tseng. Multistability for delayed neural networks via sequential contracting. IEEE Trans. Neural Netw. Learn. Syst., 26(12):3109–3122, 2015.
[4] Michael A. Cohen and Stephen Grossberg. Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Systems Man Cybernet., 13(5):815–826, 1983.
[5] Jennifer Foss, André Longtin, Boualem Mensour, and John Milton. Multistability and de- layed recurrent loops. Phys. Rev. Lett., 76:708–711, Jan 1996.
[6] J. J. Hopfield. Neurons with graded response have collective computational properties like those of two-state neurons. Proceedings of the National Academy of Sciences, 81:3088– 3092, 1984.
[7] Xiaoxin Liao and Jun Wang. Global dissipativity of continuous-time recurrent neural net- works with time delay. Phys. Rev. E (3), 68(1):016118, 7, 2003.
[8] Jui-Pin Tseng. Global asymptotic dynamics of a class of nonlinearly coupled neural net- works with delays. Discrete Contin. Dyn. Syst., 33(10):4693–4729, 2013.
[9] Jianhong Wu. Introduction to neural dynamics and signal transmission delay, volume 6 of de Gruyter Series in Nonlinear Analysis and Applications. Walter de Gruyter & Co., Berlin, 2001.
