博碩士論文 92221010 詳細資訊




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姓名 陳宣伃(Hsuan-Yu Chen)  查詢紙本館藏   畢業系所 數學系
論文名稱
(Global Exponential Stability of Modified RTD-based Two-Neuron Networks with Discrete Time Delays)
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摘要(中) 論文摘要
這篇論文主要研究離散時間遲滯的修正型RTD 雙神經元網路之全局指數穩定。在加入三種不同邊界條件後得到三組修正型RTD 雙神經元細胞網路( DCNNs )的微分方程;每一組微分方程都包含了兩個相似的細胞,每個細胞都有非線性瞬時的自身回饋,並藉由Lipshitz非線性性質與其他細胞互相連結,但卻有不同的離散時間遲滯。每組微分方程都包含外界的輸入,在自身回饋及細胞間連結長度加入適當條件後,建造適當的Lyapunov functionals ,可以驗證出其唯一平衡點具有全局指數穩定的特性;若是給定週期之外界輸入,則可驗證出每
組微分方程的週期解也具有全局指數穩定的特性。最後我們也搭配一些數值結果來驗證理論分析。
摘要(英) Abstract
In this thesis, we study the global exponential stability of the modi¯ed RTD-based two-neuron networks with discrete time delays. After imposing the periodic, Dirichlet or Neumann boundary conditions, the resulting systems consist of two identical neurons, each possessing nonlinear instantaneous self-feedback
and connected to the other neuron via a Lipschitz nonlinearity but with di®erent
discrete time delays. For each two-neuron system with constant external inputs, under appropriate conditions on the self-feedback and connection strengths, we prove the unique equilibrium is globally exponentially stable by constructing a
suitable Lyapunov functional. On the other hand, for such two-neuron systems with periodic external inputs, combining the techniques of Lyapunov functional with the contraction mapping theorem, we propose some su±cient conditions
for establishing the existence, uniqueness and global exponential stability of the periodic solutions. Numerical results are also provided to demonstrate the theoretical analyses.
關鍵字(中) 關鍵字(英) ★ equilibrium
★ periodic solution
★ global exponential stability
★ Lyapunov functional
★ discrete time delay
★ contraction mapping theorem
★ cellular neural network
論文目次 Contents
² Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1
² Periodic boundary condition . . . . . .. . . . . . . . . . . . . 3
² Dirichlet boundary condition . . . . . . . . . . . . . . . . . 13
² Neumann boundary condition . . . . .. . . . . . . . . . . . . . 17
² Concluding remarks . . . . . . . . .. . . . . . . . . . . . . . 22
² References . . . . . . . . . . . . . . . . . . . . . . . . . . 23
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指導教授 楊肅煜(Suh-Yuh Yang) 審核日期 2005-7-13
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