Chaotic and Fuzzy Study of Yin and Yang Hénon Map Systems

• Main Authors: Ho, Chun-Yen, 何俊諺
• Other Authors: Ge, Zheng-Ming
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/13563227191813280730

博士 === 國立交通大學 === 機械工程系所 === 102 === In this dissertation, various forms of nonlinear discrete Yin and Yang Hénon map systems are firstly proposed. Furthermore, their chaotic behaviors and synchronizations are investigated. The proposed Yin and Yang Hénon map system forms include: general forms, T-S fuzzy model forms, and fractional-degree forms. According to these three forms of the Yin and Yang Hénon map systems, highlights of this dissertation are as follows: First, these three Yin Hénon map system forms are firstly presented to analyze their chaotic behaviors which are compared with these three Yang Hénon map system forms by phase portraits, Lyapunov exponents and bifurcation diagrams. Second, new fractional-degree Yin and Yang Hénon map systems are firstly proposed and their chaotic behaviors are shown by calculation of Feigenbaum’s constants. Third, abundant dynamics of Yin and Yang Hénon map systems as a twin Hénon map system by attractive and repulsive couplings is shown. Finally, the T-S fuzzy model of the nonlinear chaotic Hénon map system can exactly be represented as a fuzzy aggregation of some local linear systems. The Yin Hénon map system is the inverse of Yang Hénon map system, and after T-S fuzzy modeling, state spaces of Yin and Yang Hénon map systems can be represented as linear systems. Therefore, we propose a new PDC scheme to synchronize Yin and Yang chaotic T-S fuzzy model of Hénon map systems effectively.