新延遲Ikeda-Mackey-Glass系統的渾沌、渾沌同步、渾沌控制、參數估測,與應用GYC部分區域穩定理論實現新Ikeda-Lorenz系統之渾沌廣義同步及渾沌控制

Abstract

本篇論文以相圖、分歧圖等之數值方法來研究新延遲Ikeda-Mackey-Glass系統及新Ikeda-Lorenz 系統的渾沌行為。 發現新延遲Ikeda-Mackey-Glass系統不需加入控制器,只需調整延遲項, 即可讓系統達到渾沌廣義同步、渾沌反同步及渾沌廣義延遲同步。 接著利用此新延遲Ikeda-Mackey-Glass系統之渾沌訊號, 使新延遲Ikeda-Mackey-Glass系統實現渾沌化控制。 此外本篇論文以相圖、李亞普諾夫指數等數值方法來研究新Ikeda-Lorenz 系統之渾沌行為。 並應用GYC部分區域穩定理論, 可以設計出較簡單的控制器使誤差較小。 以新Ikeda-Lorenz系統得出渾沌廣義同步及渾沌控制, 以驗證此方法之有效。最後, 利用渾沌同步使新延遲Ikeda-Mackey-Glass 系統達到參數估測之效果。根據最小平方法則, 得出系統參數之微分方程式。模擬12個微分方程式, 當系統達渾沌同步時, 使所估測的兩個參數達目標值,模擬的結果非常成功。

In this thesis, a new Ikeda-Mackey-Glass (IMG) time-delayed system and a new Ikeda-Lorenz (IL) system are studied. Their chaotic behaviors are presented by phase portraits, bifurcation diagrams, and Lyapunov exponent. When one of delay times is zero, two identical IMG systems cannot be synchronized with slightly different initial conditions. It is found that when one of delay time is positive, different types of synchronization can be obtained with slightly different initial conditions, such as generalized synchronization, anti-synchronization, and generalized lag- synchronization. One chaotization method is presented by using different types of chaos signals as parameters, it can be obtained the chaotic behaviors of a new Ikeda-Mackey-Glass time-delayed system. A new strategy to achieve chaos generalized synchronization and chaos control by GYC partial region stability theory is proposed. The control design method is simple and a less simulation error because they are in lower degree than that of traditional controllers. A new IL system is used to show the effectiveness of the scheme. Finally, estimation of parameters of a new IMG system through synchronization is studied. By a minimization problem, a system of differential equations governing the evolution of parameters is constructed. Two time delay IMG systems are synchronized and their corresponding two parameters converge to same values by solving twelve differential equations. The simulation results are very satisfactory.