Fractional Standard Map

Abstract

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 parameter of the map and the fractional order of the derivative in the original differential equation this nonlinear dynamical system demonstrates attractors (fixed points, stables 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.

8 pages, 6 figures

References in corpus (4)

• Fractional oscillator
• Fractional Equations of Kicked Systems and Discrete Maps
• Differential Equations with Fractional Derivative and Universal Map with Memory
• Long-term memory contribution as applied to the motion of discrete dynamical systems

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