非正弦力作用下非线性串联LCR电路中奇异非混沌吸引子的冒泡路径
Bubbling route to strange nonchaotic attractor in a nonlinear series LCR circuit with a nonsinusoidal force
摘要：
我们确定了一个新的路线诞生的一个奇怪的非混沌吸引子（SNA）的准周期强迫电子电路与非正弦（方波）的力作为准周期力之一，通过数值和实验研究。我们发现，气泡出现在股的准周期吸引子由于不稳定性引起的附加方波型力。然后，气泡扩大，并作为控制参数的函数而变得越来越皱。最后，气泡变得非常褶皱（而环面的其余部分基本上不受影响），导致SNA的诞生，我们称之为\emph{bubbling route to SNA}。我们从实验和数值数据的最大李雅普诺夫指数和他们的方差，庞加莱映射，傅立叶振幅谱和频谱分布函数的特征和确认这一诞生。我们还强烈证实了SNA的诞生通过冒泡路线的有限时间李雅普诺夫指数的分布。
英文摘要：
We identify a novel route to the birth of a strange nonchaotic attractor (SNA) in a quasiperiodically forced electronic circuit with a nonsinusoidal (square wave) force as one of the quasiperiodic forces through numerical and experimental studies. We find that bubbles appear in the strands of the quasiperiodic attractor due to the instability induced by the additional square wave type force. The bubbles then enlarge and get increasingly wrinkled as a function of the control parameter. Finally, the bubbles get extremely wrinkled (while the remaining parts of the strands of the torus remain largely unaffected) resulting in the birth of the SNA which we term as the \emph{bubbling route to SNA}. We characterize and confirm this birth from both experimental and numerical data by maximal Lyapunov exponents and their variance, Poincaré maps, Fourier amplitude spectra and spectral distribution function. We also strongly confirm the birth of SNA via the bubbling route by the distribution of the finite-time Lyapunov exponents.
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