In recent years, some efforts have been devoted to nonlinear dynamics of fractional discrete-time systems. A number of papers have so far discussed results related to the presence of chaos in fractional maps. However, less results have been published to date regarding the presence of hyperchaos in fractional discrete-time systems. This paper aims to bridge the gap by introducing a new three-dimensional fractional map that shows, for the first time, complex hyperchaotic behaviors. A detailed analysis of the map dynamics is conducted via computation of Lyapunov exponents, bifurcation diagrams, phase portraits, approximated entropy and C0 complexity. Simulation results confirm the effectiveness of the approach illustrated herein.

中文翻译：

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新分数离散时间系统的超混沌动力学

近年来，一些努力致力于分数离散时间系统的非线性动力学。到目前为止，许多论文已经讨论了与分数图中存在混沌有关的结果。然而，迄今为止，关于分数离散时间系统中存在超混沌的结果较少。本文旨在通过引入一种新的三维分数图来弥合差距，该图首次显示了复杂的超混沌行为。通过计算 Lyapunov 指数、分岔图、相图、近似熵和C0复杂。仿真结果证实了本文中说明的方法的有效性。