離 散 型 神 經 網 路 的 動 態 行 為

Abstract

這篇論文分成三個部份。第一個部份研究 Transiently Chaotic Neural Network (TCNN) 系統中 Transversal Homoclinic Orbit 的存在性。第二個部份利用 Lyapunov function 來研究 TCNN 的穩定性。最後一個是研究 Discrete-Time Cellular Neural Networks (DT-CNN) 的混沌現象和穩定行為。這些定性的分析與研究有助於了解各別系統可能發生的行為。

My dissertation contains three parts. The subtitle of Part I is ``Transversal Homoclinic Orbits in a Transiently Chaotic Neural Network". Transiently chaotic neural network (TCNN) was proposed by Chen and Aihara~\cite{Aihara&Chen1995Chaotic}. We prove the existence of snap-back repellers in some parameters for TCNN. And, we generalize the result on the existence of a Lyapunov function for TCNN with the constant self-feedback connection weight from symmetric connection weights to cycle-symmetric ones. The Part II is entitled ``Asymptotic Behaviors in a Transiently Chaotic Neural Network". We prove an extended version of LaSalle's invariance principle for non-autonomous difference equations. Then, we apply the LaSalle's invariance principle to TCNN with cycle symmetric connection. The subtitle of Part III is ``Dynamics for Discrete-Time Cellular Neural Networks".