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| 研究生： |
黃琮煥 Tsung-Huan Huang |
|---|---|
| 論文名稱： |
網格型動態系統行波解之研究 A Study of Traveling Wave Solutions in aLattice Dynamical System |
| 指導教授： |
許正雄
Cheng-Hsiung Hsu |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 畢業學年度： | 98 |
| 語文別： | 英文 |
| 論文頁數： | 36 |
| 中文關鍵詞： | 振盪行波解 、最終週期性行波解 、上解 、下解 |
| 外文關鍵詞： | oscillating traveling wave solutions, upper solutions, eventually periodic traveling wave solutions |
| 相關次數： | 點閱：13 下載：0 |
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此篇論文中，我們首先採用monotone iteration 的方法來研究某類網格型微分方程單調行波解的存在與多樣性。接著研究細胞神經網路行波的結構。其包含有單調性行波解、振盪性行波解與最終週期性行波解。這些結果皆是參考與推廣參考文獻[1]和[2]的研究成果。
In this thesis, we first study the existence and multiplicity results of monotonic traveling wave solutions for some lattice differential equations by using the monotone iteration method.
Then we study the structure of traveling wave solutions of
Cellular Neural Networks (CNN). The traveling wave solutions of CNN consist of monotonic traveling waves, oscillating waves and eventually periodic traveling waves. These results are survey works which extend the results of [1] and [2].
[1] C.-H. Hsu and S.-S. Lin, Existence and multiplicity of traveling waves in a lattice dynamical system, {sl J. Differential Equations} 164(2000), 431-450.
[2] C.-H. Hsu, S.-S. Lin, Traveling waves in cellular neural networks, {sl Int. J. Bifurcation and Chaos} 9, No. 7(1999), 1307-1319.
[3] I. Gyori and G. Ladas, "Oscillating theory of delay differential equations with applications", Oxford Univ. Press, Oxford, UK, 1991.
