环面加倍终端临界点附近动力学的实验观测
Experimental observation of dynamics near the torus-doubling terminal critical point.
作者信息
Bezruchko BP, Kuznetsov SP, Seleznev YP
机构信息
Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov Branch, 38, Zelyonaya Street, Saratov 410019, Russia and Department of Physics, Saratov State University, 83, Astrakhanskaya Street, Saratov 410026, Russia.
出版信息
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Dec;62(6 Pt A):7828-30. doi: 10.1103/physreve.62.7828.
A nonlinear electronic circuit driven by two signals with golden mean frequency ratio is studied. We have observed different dynamical regimes, including tori, doubled tori, strange nonchaotic attractors, and chaos, which all meet together at the critical point terminating the torus-doubling bifurcation curve (TDT point) in the parameter plane of the system. The parameter plane arrangement, spectra, and portraits of attractors observed in the experiment are in reasonable coincidence with numerical computations for a quasiperiodically forced logistic map, where the TDT critical point originally has been found and studied theoretically [S. Kuznetsov, A. Pikovsky, and U. Feudel, Phys. Rev. E 57, 1585 (1998)].
研究了由具有黄金分割频率比的两个信号驱动的非线性电子电路。我们观察到了不同的动力学状态，包括环面、双环面、奇异非混沌吸引子和混沌，它们都在系统参数平面中终止环面加倍分岔曲线（TDT点）的临界点处汇聚。实验中观察到的吸引子的参数平面排列、频谱和图像与准周期强迫逻辑斯谛映射的数值计算结果合理吻合，TDT临界点最初就是在该映射中从理论上发现并研究的 [S. 库兹涅佐夫、A. 皮科夫斯基和U. 费德尔，《物理评论E》57, 1585 (1998)]。
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