整數階與分數階雙Ikeda系統的渾沌,渾沌化及非耦合渾沌同步

Abstract

本篇論文以相圖、龐卡萊映射圖及分歧圖等數值方法研究整數階與分數階雙Ikeda系統的渾沌行為。渾沌存在於整數階與分數階雙Ikeda系統的總階數2到0.2之間，可以發現渾沌存在所有的範例中。接著研究在不同的初始條件下的兩個雙Ikeda系統延遲同步或超先同步、延遲反同步或超先反同步的現象。第一個雙Ikeda系統之渾沌現象可以藉以第二渾沌系統的渾沌狀態變量之函數取代第一個系統的延遲時間而達成。渾沌化現象也可以藉由使用第二系統的渾沌變量取代第一系統的延遲時間而獲得。最後研究兩個沒有耦合的雙Ikeda系統強健延遲渾沌同步，延遲準同步和渾沌控制，可以經由第三系統不同的渾沌狀態變量取代第一系統和第二系統的對應參數而達成。並利用不同的噪訊研究系統渾沌同步的強健度。

In this thesis, the chaotic behaviors in the integral and fractional order double Ikeda systems are studied numerically by phase portraits, Poincaré maps and bifurcation diagrams. The chaos in integral and fractional order double Ikeda systems with total order of derivatives from 2 to 0.2 are studied by phase portraits, Poincaré maps and bifurcation diagrams. It is found that chaos exists in all cases. Lag or anticipated synchronization and the lag or anticipated anti-synchronization of two double Ikeda systems with different initial conditions are discovered. By replacing their delay times by a function of chaotic state variables of a second chaotic system, the chaotic behaviors of Ikeda systems are obtained. The chaotization of a double Ikeda system is studied by using a function of state variables of a second identical system to replace the delay time of the first system. It is found that chaotization exists. Robust lag chaos synchronization, lag quasi-synchronization and chaos control of two uncoupled double Ikeda system, are achieved by replacing the corresponding parameters of two systems by different chaotic state variables of a third chaotic system. Robustness of synchronization is studied by addition of various noises. The results are satisfactory.