| Summary: | 博士 === 中原大學 === 機械工程研究所 === 95 === 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.
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