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首页> 外文期刊>Discrete and continuous dynamical systems▼hSeries S >MULTI-DIRECTIONAL AND SATURATED CHAOTIC ATTRACTORS WITH MANY SCROLLS FOR FRACTIONAL DYNAMICAL SYSTEMS
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MULTI-DIRECTIONAL AND SATURATED CHAOTIC ATTRACTORS WITH MANY SCROLLS FOR FRACTIONAL DYNAMICAL SYSTEMS

机译：多向和饱和混沌吸引子，具有许多用于分数动力系统的卷轴

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摘要

Chaotic dynamical attractors are themselves very captivating in Science and Engineering, but systems with multi-dimensional and saturated chaotic attractors with many scrolls are even more fascinating for their multidirectional features. In this paper, the dynamics of a Caputo three-dimensional saturated system is successfully investigated by means of numerical techniques. The continuity property for the saturated function series involved in the model preludes suitable analytical conditions for existence and stability of the solution to the model. The Haar wavelet numerical method is applied to the saturated system and its convergence is shown thanks to error analysis. Therefore, the performance of numerical approximations clearly reveals that the Caputo model and its general initial conditions display some chaotic features with many directions. Such a chaos shows attractors with many scrolls and many directions. Then, the saturated Caputo system is indeed chaotic in the standard integer case (Caputo derivative order α=1) and this chaos remains in the fractional case (α= 0.9). Moreover the dynamics of the system change depending on the parameter α, leading to an important observation that the saturated system is likely to be regulated or controlled via such a parameter.
机译：混沌动态吸引子本身非常迷住于科学和工程，但是具有许多卷轴的多维和饱和混沌吸引子的系统对于它们的多向功能来说更加令人着迷。本文通过数值技术成功研究了Caputo三维饱和系统的动态。模型中涉及饱和功能系列的连续性属性促进了适当的分析条件，用于对模型解决方案的存在性和稳定性。 HAAR小波数值方法应用于饱和系统，并且由于误差分析而显示其收敛。因此，数值近似的性能明显揭示了Caputo模型及其一般初始条件显示了许多方向的一些混沌特征。这样的混乱显示出许多卷轴和许多方向的吸引子。然后，饱和的Caputo系统确实在标准整数情况下混乱（Caputo衍生阶α= 1），并且该混沌保留在分数壳体中（α= 0.9）。此外，根据参数α改变系统的动态，导致饱和系统可能通过这种参数调节或控制饱和系统。

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