分數階Newton-Leipnik系統之非線性動態及混沌控制

Nonlinear ndynamics and chaotic control of Newton-Leipnik system with fractional order

林廣台(Kuang-Tai Lin)

指導教授 ： 康淵

中原大學/工學院/機械工程學系/博士(2007年)

https://doi.org/10.6840/cycu200700181

摘要

分數階系統之動態特性已在近幾年引起廣泛的研究。本論文中應用數值分析深入探討分數階Newton-Leipnik系統之非線性動態與混沌，主要分為兩個研究項目；(1)分析該系統是否會產生混沌現象並研究其動態特性，以及系統參數變化對系統動態特徵的影響；(2)利用上述分析結果，對系統進行混沌控制。研究結果顯示系統展現複雜之動態行為，例如：穩定狀態、週期運動(包含倍週期與週期3)、限循環、混沌及暫態混沌。研究中不但證實分數階系統有混沌現象，而且階數低於3，最低階數可達2.82。同時，系統參數變化對系統的動態特徵亦有重要之影響。此外，應用四種不同的線性回饋訊號，對系統做混沌控制，亦得到良好之結果。

關鍵字

倍週期 ； 暫態混沌 ； 限循環 ； 分數階系統 ； Newton-Leipnik系統 ； 混沌

並列摘要

The dynamics of fractional-order systems have attracted a great deal of attentions in recent years. In this paper, two main subjects have been comprehensively studied numerically. One is to find out whether the chaotic motions exist in the Newton-Leipnik system with a fractional order and to observe its dynamical behaviors, also to investigate the influences of change of parametric values on this system; and the other is to perform the chaos control on this fractional-order system. The system displays complex dynamical behaviors, such as fixed points, limit cycle, periodic motions (including period-3 motions), chaotic motions, and transient chaos. Most important, it has been found that chaos exists in the fractional-order system with order less than 3. In this study, the lowest order for this system to yield chaos is 2.82. Meanwhile, the variations of parameters also exhibit the significant effects on this system. In addition, the chaos controlling is performed by a static linear feedback controller with four different types of signal.

並列關鍵字

Newton-Leipnik system ； transient chaos ； period doubling ； chaos ； limit cycle ； fractional order system

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