Dynamics in Discrete-Time Neural Networks

• Main Authors: Chen Shyan Shiou, 陳賢修
• Other Authors: Shih Chih Wen
• Format: Others
• Language: en_US
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/54457770570109070420

博士 === 國立交通大學 === 應用數學系 === 90 === 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".