Fractional standard map

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• 作者：Mark Edelman ; Vasily E. Tarasov
• 关键词：Discrete map ; Fractional differential equation ; Attractor
• 刊名：Physics Letters A
• 出版年：2009
• 出版时间：28 December 2009
• 年：2009
• 卷：374
• 期：2
• 页码：279-285
• 全文大小：572 K

文摘

Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the map parameter and the fractional order of the derivative in the original differential equation, this nonlinear dynamical system demonstrates attractors (fixed points, stable periodic trajectories, slow converging and slow diverging trajectories, ballistic trajectories, and fractal-like structures) and/or chaotic trajectories. At least one type of fractal-like sticky attractors in the chaotic sea was observed.