複數網格型耦合系統在Julia集上的同步化

Abstract

本篇論文主要目的是為了解決Julia集上複數耦合網格系統（Complex Valued Coupled Map Lattices（CCMLs））的同步現象。首先，我們介紹一個研究全域同步與局部同步的統一形式。其次，我們解決一個 inf min max的問題，這個問題，是在給定的一群耦合矩陣中，找到一個耦合矩陣和其相對應的耦合係數使得系統的同步收斂速度最快。最後，我們給出對應系統在Julia集上的全域同步與局部同步之結果。

The purpose of this thesis is to address synchronous chaos on a Julia set in complex-valued coupled map lattices (CCMLs). Our main results contain the following. First, a unified formulation for the study of global and local synchronization CCMLs is presented. Second, we solve an inf min max problem for which its solution gives the fastest synchronized rate among a class of coupling matrices. Third, various results for global and local synchronization on the Julia set are presented.