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INFINITE NUMBER OF PARAMETER REGIONS WITH FRACTAL NONCHAOTIC ATTRACTORS IN A PIECEWISE MAP
Fractals ( IF 4.7 ) Pub Date : 2021-04-30 , DOI: 10.1142/s0218348x21500870
TAO CHENG 1 , YONGXIANG ZHANG 2 , YUNZHU SHEN 3
Affiliation  

We identify a countable infinity of parameter regimes with strange nonchaotic attractors (SNAs). At the edge of each arc parameter area, there is an uncountable infinity of SNAs with torus intermittency. The mechanism for the creation of SNAs in different regime is induced by an n-frequency quasiperiodic orbit through a quasiperiodic analog of saddle-node bifurcation (Type-I intermittent route). We describe the transition between tori and SNAs by the largest Lyapunov exponent and phase diagram. These SNAs are characterized by the phase sensitivity exponents, rational approximations, singular-continuous spectra, and distribution of finite-time Lyapunov exponents.

中文翻译:

分段地图中具有分形非混沌吸引子的无限数量的参数区域

我们确定了具有奇怪的非混沌吸引子 (SNA) 的可数无穷大参数方案。在每个圆弧参数区域的边缘,都有无数个具有环面间歇性的 SNA。在不同制度下创建 SNA 的机制是由一个n-频率准周期轨道通过鞍节点分岔的准周期模拟(类型-一世间歇路线)。我们通过最大的李雅普诺夫指数和相图描述了环面和 SNA 之间的过渡。这些 SNA 的特征在于相位灵敏度指数、有理逼近、奇异连续光谱和有限时间 Lyapunov 指数的分布。
更新日期:2021-04-30
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