渾沌與鳥群行為控制，渾沌廣義及交織同步與超渾沌

Abstract

本篇論文以相圖、龐卡萊映射圖、Lyapunov 指數、分歧圖以及參數圖等數值方法研究慣性測速器系統的渾沌現象。對此系統研究應用GYC部分區域穩定理論來研究系統的廣義渾沌同步和渾沌控制。以非自治慣性測速器系統來模擬鳥群的渾沌行為。此外，將探討Lorenz 系統以Bessel 函數為參數的渾沌及超渾沌行為。最後透過非線性方法來研究非自治系統的交織同步。在以上研究中，皆可由相圖和時間歷程圖得到驗證。

In this thesis, the chaotic behavior in an inertial tachometer system is studied by phase portraits, time histories, Poincaré maps, Lyapunov exponents, bifurcation diagram and parametric diagram. A new strategy to achieve chaos generalized synchronization and chaos control by GYC partial region stability theory is proposed Boids control of chaos for a nonautonomous inertial tachometer system is presented. Moreover, the Lorenz system with Bessel function parameters is studied for chaotic and hyperchaotic behaviors. Finally, a new symplectic synchronization of different order nonautonomous systems via nonlinear control is studied. Numerical analysis, such as phase portraits and time histories can be provided to verfy the effectiveness in all above studies.