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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/48040完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 林紹雄 | |
| dc.contributor.author | Yi-Hung kuo | en |
| dc.contributor.author | 郭一鴻 | zh_TW |
| dc.date.accessioned | 2021-06-15T06:44:57Z | - |
| dc.date.available | 2011-07-07 | |
| dc.date.copyright | 2011-07-07 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-06-28 | |
| dc.identifier.citation | [1] D. Barkley, Linear stability analysis of rotating spiral waves in excitable media, Phys. Rev. Lett. 68, 2090-2093(1992).
[2] D. Barkley, Euclidean symmetry and the dynamics of rotating spiral waves, Phys. Rev. Lett. 72, 164-167(1994). [3] D. Henry, Geometric theory of semilinear parabolic equations, Springer, 1975. [4] A. N. Zaikin, A. M. Zhabotinsky, Nature(London) 225, 535(1970). [5] J. M. Davidenk, A.V. Pertsov, R. Salomonsz, W. Baxter, J. Jalife, Nature(London) 355, 349(1992). [6] F. Siegert, C. Weijer, J. Cell. Sci. 93, 325(1989). [7] S. Jakubith, H. H. Rotermund, W. Engel, A. von Oertzen, G. Etrl, Phys. Rev. Lett. 65, 3013(1990). [8] J. Lechleiter, S. Girard, E. Peralta, D. Clapham, Science 252 23(1991). [9] N. A. Gorelova, J. Bures, J, Neurobiol. 14 353(1983) [10] E. Yanagida, Existence of periodic travelling wave solutions of reaction-diffusion systems with fast-slow dynamics, J. Diff. Eq. 76, 115-134(1988) [11] J. Evans, The stability of nerve impulses, I linear approximations, Indiana Univ. Math. J. 21, 877-885(1972) [12] J. Evans, The stability of nerve impulses, II stability at rest, Indiana Univ. Math. J. 22, 75-90(1972) [13] J. Evans, The stability of nerve impulses, III stablity of the nerve impulse, Indiana Univ. Math. J. 22, 577-593(1972) [14] C. K. R. Jones, Stability of the travelling wave solution of the FitzHugh-Nagumo system, Transactions of the American mathematical society, 286, 431-469(1984) [15] C. K. R. T. Jones, N. Kopell, Tracking invariant manifolds with differential forms in singularly perturbed systems, J. Diff. Eq. 108, 64-88(1994). [16] N. Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J. 21, 193-226(1971) [17] N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, Indiana Univ. Math. J. 31, 53-98(1979) [18] D. S. Cohen, J. C. Neu and R. R. Rosales, Rotating spiral wave solutions of reactiondiffusion equations, SIAM J. Appl. Math. 35, 536-547(1978) [19] B. Fiedler, B. Sandstede, A. Scheel, and C. Wulff, Bifurcation from relative equilibria to non-compact group actions: skew products, meanders, and drifts. Doc. Math. J. DMV, 1, 479-505(1996) [20] C. Wulff, Transitions from relative equilibria to relative periodic orbits, Documenta Math. 5, 227-274(2000) [21] R. Kapral, K. Showalter (Eds.), ”Chemical waves and patterns”, Kluwer Academic Publishers, 1995. [22] L. N. Trefethen, Spectral methods in Matlab, SIAM, 2001. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/48040 | - |
| dc.description.abstract | 本篇論文中，以geometric singular perturbation法證明，Barkley系統有一維的脈衝解，再以數值法檢驗此脈衝解在有外力微擾下的行為。同時也會以數值法觀察二維的迴旋波解。 | zh_TW |
| dc.description.abstract | In this thesis, the existence of travelling pulse solution of Barkley system in one spatial dimension is proved via the method of geometric singular perturbation. The stability of such travelling pulses are tested numerically. Spiral waves in two spatial dimension are also studied numerically. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T06:44:57Z (GMT). No. of bitstreams: 1 ntu-100-R98221007-1.pdf: 2216365 bytes, checksum: bda6ed0566f4e4aef1cd8604ef4d48ca (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | 1 Introduction 1
2 Excitability 4 3 Travelling pulses 9 3.1 Fast and slow systems 9 3.2 Homoclinic singular orbits 11 3.3 The method of geometric singular perturbation 13 3.4 Stable and unstable manifolds 15 3.5 Main results and proofs 18 3.6 Numerical simulations 20 4 Spiral waves 24 4.1 Governing equations 24 4.2 Numerical simulations 25 5 Conclusions 28 A Numerical scheme 29 | |
| dc.language.iso | en | |
| dc.title | Barkley系統的旅行波和迴旋波解 | zh_TW |
| dc.title | Barkley system | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 林太家,羅主斌 | |
| dc.subject.keyword | 微擾法,旅行波,脈衝波,迴旋波,反應擴散,擬譜方法, | zh_TW |
| dc.subject.keyword | geometric singular perturbation,travelling wave,spiral wave,travelling pulse,reaction-diffusion equation,pseudospectral method, | en |
| dc.relation.page | 32 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2011-06-28 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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