本篇論文致力於了解兩個相同的若斯勒超混沌系統(Rossler hyperchaotic systems)，經由某些參數耦合所組成的混沌系統裡的同步現象。在證明兩系統的同步現象，需引入一適當的黎阿普諾夫函數(Lyapunov function)，並配合相關定理來映證，當耦合係數（coupling coefficients）充分大時，我們更可以證明出兩混沌系統之同步性。此外，針對這份研究的目的，我們除了整理相關文獻裡出現的黎阿普諾夫函數(Lyapunov function)定義、定理外，也將此規則應用於我們的證明中。甚且，在論文的最後將藉由一連串的數值結果來展示(1)兩若斯勒超混沌系統的耦合同步現象(2)若斯勒系統的黎阿普諾夫指數(Lyapunov exponents)(3)若斯勒超混沌系統的吸引子投影圖。

In this paper, we propose the sychronizaion of the two coupled Rossler systems. First, we construct a specific Lyapunov function to check the sychronizaion of the two coupled systems. Through the construction of Lyapunov function we can see that the two coupled systems will be synchronized under some certain circumstances. Second, we will display the numerical results to show the effectiveness of synchronization, the Lyapunov exponents of the Rossler systems, and projections of Rossler's hyperchaotic attractor with different parameters.

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