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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：154 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。
We study multistable Hopfield-type neural networks with delays in this paper. We illustrate the idea of our approach by considering the networks which consist of two neurons. From the geometric configuration of equations, we derive various criteria which lead to disparate numbers of equilibria. We can further establish the convergence of dynamics for the networks.
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.
