Chaos in the Newton-Leipnik System with Fractional Order

分數階牛頓－勞伯尼克系統混沌分析

10.6989/JN.201112.0061

林廣台(Kuang-Tai Lin)；朱朝煌(Chau-Hwang Chu)

分數階 ； 牛頓－勞伯尼克系統 ； 混沌運動 ； 暫態混沌 ； fractional-order ； Newton-Leipnik system ； chaotic motions ； transient chaos

南亞學報

31期（2011 / 12 / 01）

61 - 71

英文

近年來分數階系統動力學受到長足的關注。本文針對分數階牛頓－勞伯尼克系統的動力學作數值研究。系統顯示許多有趣的動力行為，例如固定點，週期運動、混沌運動和暫態混沌，在分數階系統中當階次小於3時發現混沌的存在。本研究系統能產生混沌的最低階次為2.82，在分數階系統中同時也發現到混沌週期2的軌跡。

The dynamics of fractional-order systems has attracted increasing attention in recent years. In this paper, the dynamics of the Newton-Leipnik system with fractional order was studied numerically. The system displays many interesting dynamic behaviors, such as fixed points, periodic motions, chaotic motions, and transient chaos. It was 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. A period-doubling route to chaos in the fractional-order system was also found.