博碩士論文 90221004 詳細資訊




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姓名 林嫺雯(Shian-Wen Lin)  查詢紙本館藏   畢業系所 數學系
論文名稱 遲滯型細胞神經網絡行進波之結構
(Structure of Traveling Waves in Delayed Cellular Neural Networks)
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摘要(中) 這篇論文主要研究,在一個維度上,遲滯型細胞神經網絡
(CNN)行進波解的結構。利用Monotone Iteration 及
Shooting的方法我們可以證明行進波之解結構隨著速度的改變而有不同的行為。
摘要(英) This thesis is concerned with the global structure of traveling waves
for one-dimensional cellular neural networks with distributed delayed signal
transmission. By using the monotone iteration method and shooting
method, we describe the transition of wave profiles from monotonicity,
damped oscillation, periodicity, unboundedness and back to monotonicity
as the wave speed is varied.
關鍵字(中) ★ 細胞神經網絡
★ 行進波
關鍵字(英) ★ cellular neural networks
★ traveling waves
論文目次 Abstract.........................................................................1
1. Introduction.............................................................2
2. Properties of Characteristic Equation.....................5
3. Existence of Monotonic Traveling Waves................7
3.1. Construction of Upper and Lower Solutions.....7
3.2. Monotone Iteration Method.............................11
3.3. Proof of Main Theorem (I)..............................14
4. Structure of Non-Monotonic Traveling Waves.......15
4.1. Basic Properties of Asymptotic Initial Value
Problem...................................................................15
4.2. Proof of Main Theorem (II)............................26
References.....................................................................28
參考文獻 [1] S.-N. Chow, J. Mallet-Paret, and W. Shen, Traveling waves in lattice dynamical
systems, J. Di . Eqns., 149 (1998), pp. 248-291.
[2] L. O. Chua, CNN: A Paradigm for Complexity, World Scientific Series on
Nonlinear Science, Series A, Vol. 31, World Scientific, Singapore, 1998.
[3] L. O. Chua and T. Roska, The CNN paradigm, IEEE Trans. Circuits Syst.,
40 (1993), pp. 147-156.
[4] L. O. Chua and L. Yang, Cellular neural networks: Theory, IEEE Trans.
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[5] L. O. Chua and L. Yang, Cellular neural networks: Applications, IEEE
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[6] T. Erneux and G. Nicolis, Propagation waves in discrete bistable reactiondi
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[7] I. Gyori and G. Ladas, Oscillating Theory of Delay Di erential Equations
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[8] C.-H. Hsu and S.-S. Lin, Existence and multiplicity of traveling waves in a
lattice dynamical system, J. Di . Eqns., 164 (2000), pp. 431-450.
[9] C.-H. Hsu, S.-S. Lin and W. Shen, Traveling waves in cellular neural networks,
Internat. J. Bifur. and Chaos, 9 (1999), pp. 1307-1319.
[10] C.-H. Hsu and S.-Y. Yang, On camel-like traveling wave solutions in cellular
neural networks, preprint, 2002.
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[14] J. Mallet-Paret, The global structure of traveling waves in spatial discrete
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pp. 291-296, Seville, Spain, June 24-26, 1996.[16] P. Thiran, K. R. Crounse, L.O. Chua, and M. Hasler, Pattern formation
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[17] P. Thiran, Dynamics and Self-Organization of Locally Coupled Neural
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[18] F. Werblin, T. Roska and L.O. Chua, The analogic cellular neural network
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[19] P. Weng and J. Wu, Deformation of traveling waves in delayed cellular
neural networks, preprint, 2001.
[20] J. Wu and X. Zou, Asymptotical and periodic boundary value problems
of mixed FDEs and wave solutions of lattice di erential equations, J. Di .
Eqns., 135 (1997), pp. 315-357.
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指導教授 許正雄(Cheng-Hsiung Hsu) 審核日期 2003-6-29
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