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。 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.
