博碩士論文 102221603 完整後設資料紀錄

DC 欄位 語言
DC.contributor數學系zh_TW
DC.creator黃亞妮zh_TW
DC.creatorPuji Andayanien_US
dc.date.accessioned2014-7-15T07:39:07Z
dc.date.available2014-7-15T07:39:07Z
dc.date.issued2014
dc.identifier.urihttp://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=102221603
dc.contributor.department數學系zh_TW
DC.description國立中央大學zh_TW
DC.descriptionNational Central Universityen_US
dc.description.abstract此篇論文主要研究某類三維癌症模型的整體穩定性。此模型主要是描述宿主細胞、免疫效應細胞及腫瘤細胞之間的影響。根據所考慮的參數,此模型最多有 七個孤立的平衡點。我們首先給出保證各個平衡點存在的充分條件。同時我們證明當起始值位於第ㄧ卦限時模型解的有界性。接著我們利用常微分方程標準的方法及中心流形理論探討平衡點的線性穩定性。我們可以將所考慮的參數分為兩大類來探討平衡點的線性穩定性。此模型於其中一類參數考慮下並不存在正的平衡點,我們進一步嚴格證明此模型解的行為終將收斂至邊界的平衡點。同時我們提供一些數值結果驗證所得之理論成果。對於另ㄧ類參數,我們則提供了一些數值結果。從數值結果顯示此模型解在不同參數下,不僅俱有整體穩定性之特性同時亦呈現出解的混沌現象。zh_TW
dc.description.abstractIn this thesis, we consider the global stability for some three dimensional cancer model which describes interaction between the host cells, the effector immune cells, and the tumor cells. According to the parameters on the models, there are at most seven isolated equilibria. We first provide some sufficient conditions that guarantee the existence of various kinds of positive equilibria for the system. Then we show that all solutions of the system are bounded when the initial data belong to the first quadrant. Next, we analyze the local stability of the equilibria by using the standard method of ODE and center manifold theory. The linearized stability result can be haracterized by two categories of the parameters. In one of the categories, there exists no positive equilibrium and we rigorously prove that all solutions trajectories converge to the boundary equilibria. We also perform some numerical simulations to support the main results. For another category, we provide some numerical results which demonstrate not only the global stability behavior but also the existence of chaotic phenomena.en_US
DC.subject宿主細胞zh_TW
DC.subject免疫效應細胞zh_TW
DC.subject腫瘤細胞zh_TW
DC.subject中心流形理論zh_TW
DC.subjectDulac 標準zh_TW
DC.subjectPoincaré-Bendixson 定理zh_TW
DC.subjectomega-極限集zh_TW
DC.subjecthost cellsen_US
DC.subjecteffector-immune cellsen_US
DC.subjecttumor cellsen_US
DC.subjectcenter manifold theoryen_US
DC.subjectDulac’s criterionen_US
DC.subjectPoincar´e-Bendixson theoremen_US
DC.subjectomega-limit seten_US
DC.title某類三維癌症模型之整體穩定性分析zh_TW
dc.language.isozh-TWzh-TW
DC.titleGlobal Stability Analysis for Some Three-Dimensional Cancer Modelsen_US
DC.type博碩士論文zh_TW
DC.typethesisen_US
DC.publisherNational Central Universityen_US

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