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標題: 反應-擴散問題之多重分支
Multiple Bifurcations in a Reaction-diffusion Problem
作者: 陳美華
Chen, Mei-Hwa
出版社: 應用數學系
摘要: 我們研究一組反應-擴散方程式的多重分支,以及使用數值方法追蹤分支. 我們指出,經由兩個雙重分支的模式交互作用,我們可以得到共秩為四的分 支點.我們證明一個具多重參數的分支問題,只要適當的選取參數,一個多 重分支點之多重性經由離散化之後仍可被保留下來.經由此我們可以降低 分支的不完全性.我們亦使用一個延續-BCG的算則求解分支.最後,我們用 布魯塞爾方程式做數值試驗,且對結果提出報告.
We study multiple bifurcations in a system of reaction-diffusion equations defined on the unit square. First, we investigate linear stability of thesystem at the uniform steady state solution. Then we discuss necessary conditions for mode interactions. In particular, we show that a corank-four bifurcation point of the system can be easily generated by the mode interactions of two double bifurcation points. We also study the possibilities of preserving the multiplicity of bifurcation points in the discrete system. A continuation-BCG algorithm proposed by Chien et al. is exploited to trace the solution branches. Finally, sample numerical results are reported.
Appears in Collections:應用數學系所



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