Period-doubling cascades and devil's staircases of the driven van der Pol oscillator.
Period-doubling cascades and devil's staircases of the driven van der Pol oscillator.
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DOI：
10.1103/physreva.36.1428
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发表时间：
1987-08
期刊：
影响因子：
--
通讯作者：
U. Parlitz;Werner Lauterborn
中科院分区：
文献类型：
--
作者：
U. Parlitz;Werner Lauterborn
给出了驱动货车der Pol振荡器的分岔图，显示了锁模和倍周期级联。在低驱动幅度锁定区域发生以下Farey序列。在高驱动振幅，这种关系被破坏，由于倍周期级联和共存的吸引子的外观。本文利用缠绕数的推广计算了倍周期叶栅的魔鬼阶梯和缠绕数图。倍周期分叉点处的绕组数构成一个交替序列，该序列在级联的聚点处收敛。
Bifurcation diagrams of the driven van der Pol oscillator are given showing mode-locking and period-doubling cascades. At low driving amplitudes locking regions occur following Farey sequences. At high driving amplitudes this relationship is destroyed due to the appearance of period-doubling cascades and coexisting attractors. A generalization of the winding number is used to compute devil's staircases and winding-number diagrams of period-doubling cascades. The winding numbers at the period-doubling bifurcation points constitute an alternating sequence that converges at the accumulation point of the cascade.