DSpace Collection:
https://ah.lib.nccu.edu.tw/handle/140.119/43
2024-03-28T17:01:18Z一類耦合系統的同步行為
https://ah.lib.nccu.edu.tw/handle/140.119/115311
題名: 一類耦合系統的同步行為
摘要: 在這近幾十年來,耦合系統的同步化行為已經成為相當重要的研究課題。在現有文獻中,用來處理具時間延遲之非線性耦合系統同步化問題的方法仍受到了相當的限制。現有處理非線性藕合系統同步問題的方法大多要求耦合矩陣是與時間無關的、或對稱的,或者要求耦合矩陣之行的總和須為零、或其非對角線元素必須為非負,並且要求耦合函數的斜率必須大於某一個正數。在這個研究中,我們發展出一套可以處理具更一般耦合矩陣形式並具一般形式的耦合函數之具時間延遲的非線性耦合系統的同步化方法。; Synchronization of coupled systems have been important research topics in recent decades. In the literature, the existing methods for the synchronization of nonlinearly coupled systems with delay are still limited. Most of the existing approaches to the synchronization problems of nonlinearly coupled systems require the connectivity matrix to be time-independent, symmetric, with zero row-sums, with nonnegative off-diagonal entries; moreover, these approaches commonly require that the coupling functions have positive lower bounds on their slope. In this project, we develop an approach to the synchronization of nonlinearly coupled systems with delays. Under this approach, the connection matrix could be quite general, and the condition on the slope of the coupling functions, which is commonly imposed on the coupling functions in the existing approaches, is not necessary2017-12-22T06:55:44Z耦合系統的全局動態行為之研究及其在生物模型上的應用
https://ah.lib.nccu.edu.tw/handle/140.119/115088
題名: 耦合系統的全局動態行為之研究及其在生物模型上的應用
摘要: 在這近幾十年來,耦合系統的同步化行為與多重穩定性已經成為相當重要的研究課題。在現有文獻中,用來處理線性耦合系統同步化問題的方法往往依賴於特定的耦合形式;也因此它們的應用往往受到了限制。現有處理同步問題的方法大多要求耦合矩陣是與時間無關的、或對稱的,或者要求耦合矩陣之行的總和須為零、或其非對角線元素必須為非負、或其所有非零特徵值需具有負實部、或滿足節點的平衡等等。在這個研究中,我們發展出一套可以處理具更一般耦合矩陣形式之耦合系統的同步化方法。另外在這個研究中,我們也發展一個可處理具多重穩定平衡點之神經網路的全局收斂性的方法;此方法可適用於具平滑的S形(sigmoidal)耦合函數或分段線性耦合函數。經由此方法,我們可推導了具各種不同平衡點個數的條件,並研究系統的收斂性。; Synchronization and multistability of coupled systems have been important research topics in recent decades. In the literature, much of the existing methods for the synchronization of coupled systems strong rely on specific forms of the coupling structure; their applications are consequently limited. Most of the existing approaches to the synchronization problems require the connectivity matrix to be time-independent, symmetric, with zero row-sums, with nonnegative off-diagonal entries, with all nonzero eigenvalues having negative real part, or with node balance, etc. In this project, we develope an approach to the synchronization of a network of coupled oscillators under which the connection matrix could be quite general. Moreover, we also develope a new approach to conclude the global convergence to multiple equilibrium points of the neural networks. This approach accommodates both smooth sigmoidal and piecewise linear activation functions. Based on this approach, we derive several criteria which lead to disparate numbers of equilibria, and investigate the convergence of the systems2017-12-08T07:01:28Z基於結構關聯分析之模糊資料型的財經時間數列相關程度探討
https://ah.lib.nccu.edu.tw/handle/140.119/115087
題名: 基於結構關聯分析之模糊資料型的財經時間數列相關程度探討
摘要: 本研究計畫首先探討關聯結構理論之技術工具,如關聯結構對財金經濟資料聯合分配偏態的影響,關聯結構模型的估計,關聯結構模型選擇等。接著探討關聯結構理論與投資組合管理關聯,最佳模式選取策略與穩定參數之估計。並發展出一套能對於財金經濟資料或資產價格聯合分配合理假設的方法。最後以實證資料(數據及非數據)分析,提出模糊相關係數的估算。並比較關連結構與模糊相關係數的優缺點,對相關係數資產分配有更妥適的描述,如投資組合管理、風險管理及衍生性金融商品訂價策略,以及提升財務分析的可靠度。; This research proposal aims at investigating structure dependence for financial/economic time series with emphasis on imprecise data such as fuzzy data. The current practice in, say, forecasting economic phenomena from observed time series data, is based upon the methods of copulas and their optimization techniques such as maximum entropy. This can be achieved when data are precise. However, observed time series data in econometrics/finance are often coarse, i.e. of low quality, due to errors in measurements, missing data, sample selection, imprecision in observations. We propose to investigate the use of copula techniques for coarse data on this research project. And compare off even the structure and the advantages and disadvantages of the fuzzy correlation coefficient, the asset allocation of the correlation coefficient is more properly described, such as portfolio management, risk management and financial derivatives pricing strategies, as well as to enhance the reliability of financial analysis. Application domains: Risk management in financial econometrics, actuarial sciences, credit management decision.2017-12-08T07:01:14Z一維 Emden-Fowler 型半線性波方程式解之存在區間之估計
https://ah.lib.nccu.edu.tw/handle/140.119/115086
題名: 一維 Emden-Fowler 型半線性波方程式解之存在區間之估計
摘要: In this report we will review some results on Emden-Fowler equations and treat the estimates for the life-span of positive solutions of some semi-linear wave equations with initial and boundary values problem in bounded domain. And in the last, we report some recently result on the blow-up phenomenon of Emden-Fowler type semilinear wave equation.2017-12-08T07:01:00Z