新渾沌系統之超渾沌、智慧型模糊控制、廣義渾沌同步與陰陽渾沌

Abstract

本論文探討渾沌系統之超渾沌現象，首次提出並研究陰陽渾沌。採用新模糊模型、新模糊控制器、 GYC部份區域穩定理論以及實用漸進穩定理論來達到廣義渾沌同步。主要研究重點如下： 1.分析經典Lorenz 系統的陰渾沌，並與其系統的陽渾沌做對比研究。 2.新Mathieu-van der Pol 系統超渾沌現象的研究。運用相圖、功率頻譜圖、李亞普諾夫指數以及二維和三維參數圖來分析其渾沌行為。就四狀態變量系統，發現三個正李亞普諾夫指數。 3.運用GYC部份穩定理論以達到系統之渾沌控制和適應性渾沌同步。 4.提出只須兩個線性子系統即能表達複雜渾沌行為的新模糊模型，並用以達成複雜系統以及不同系統之渾沌同步。 5.提出常數模糊控制器的簡化概念，運用其完滿達成廣義同步。

Hyperchaos of chaotic systems, Yin-Yang chaos, new fuzzy model, new fuzzy logic controllers, generalized chaos synchronization via GYC partial region stability theory and pragmatical asymptotically stability theorem are studied in this thesis. The main points in the researches are shown as follow: 1.Analyzing Yin chaos of the classical Lorenz system and comparing it with Yang chaos. 2.Hyperchaos in a new Mathieu-van der Pol system is identified by phase portraits, power spectrum, Lyapunov exponents and 2-D and 3-D parameters diagrams. Three positive Lyapunov exponents are found for system with four states. 3.Chaotic control and synchronization for a system by GYC partial region theory. 4.New fuzzy model is proposed to simulate the complicated chaotic behaviors via only two linear subsystems and used to carry out synchronization of complicated chaotic systems and different chaotic systems. 5.Simplified fuzzy logic constant controller (FLCC) is presented to achieve generalized synchronization.