1. NCCU Academic Hub
  2. 學術產出
  3. College of Science
  4. Theses
  5. Item

學術產出-Theses

Article View/Open

Publication Export

Google ScholarTM

政大圖書館

Citation Infomation

  • No doi shows Citation Infomation
題名 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
作者 陳冠瑋
Chen, Guan-Wei
貢獻者 曾睿彬
Tseng, Jui-Pin
陳冠瑋
Chen, Guan-Wei
關鍵詞 神經網路
多重穩定性
時間延遲
收斂性
日期 2017
上傳時間 5-Apr-2017 15:36:48 (UTC+8)
摘要 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。
參考文獻 [1] Nikola Burić and Dragana Todorović. Dynamics of fitzhugh-nagumo excitable systems with delayed coupling. Phys. Rev. E, 67:066222, Jun 2003.
[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.
描述 碩士
國立政治大學
應用數學系
103751015
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0103751015
資料類型 thesis
dc.contributor.advisor 曾睿彬zh_TW
dc.contributor.advisor Tseng, Jui-Pinen_US
dc.contributor.author (Authors) 陳冠瑋zh_TW
dc.contributor.author (Authors) Chen, Guan-Weien_US
dc.creator (作者) 陳冠瑋zh_TW
dc.creator (作者) Chen, Guan-Weien_US
dc.date (日期) 2017en_US
dc.date.accessioned 5-Apr-2017 15:36:48 (UTC+8)-
dc.date.available 5-Apr-2017 15:36:48 (UTC+8)-
dc.date.issued (上傳時間) 5-Apr-2017 15:36:48 (UTC+8)-
dc.identifier (Other Identifiers) G0103751015en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/108119-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學系zh_TW
dc.description (描述) 103751015zh_TW
dc.description.abstract (摘要) 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。zh_TW
dc.description.tableofcontents 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		zh_TW
dc.format.extent 3572277 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0103751015en_US
dc.subject (關鍵詞) 神經網路zh_TW
dc.subject (關鍵詞) 多重穩定性zh_TW
dc.subject (關鍵詞) 時間延遲zh_TW
dc.subject (關鍵詞) 收斂性zh_TW
dc.title (題名) 具時間延遲之霍普菲爾神經網路的多重穩定性zh_TW
dc.title (題名) Multistability in Hopfield-type neural networks with delaysen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] Nikola Burić and Dragana Todorović. Dynamics of fitzhugh-nagumo excitable systems with delayed coupling. Phys. Rev. E, 67:066222, Jun 2003.
[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.		zh_TW