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Chaos from phase-locked loops. High-dissipation case

机译:锁相环的混乱。高耗散案例

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For pt.I see ibid., vol.35, no.8, p.987-1003, 1988. The numerical calculations of theorem 2 of pt.I which gives the homoclinicity condition for the non-Hamiltonian, i.e. dissipative, unperturbed case, are performed. In particular, many boundary curves which identify the homoclinic tangency and show that there exists a homoclinic orbit above the curves but no homoclinic orbit below them are obtained. Moreover, the associated Poincare maps (obtained by Runge-Kutta-Gill simulation) confirm that the homoclinicity condition predicted from these diagrams is correct. Finally, computer simulation is used to obtain the actual chaotic attractors observed from a very small external sinusoidal force. This corresponds exactly to the experimental results reported in pt.I that the chaotic phenomena observed from actual experiments in pt.I is indeed a horseshoe chaos based on a homoclinic orbit.
机译:对于pt.I,请参见同上,第35卷,第8期,第987-1003页,1988年。pt.I定理2的数值计算给出了非哈密顿量(即耗散,无扰动情况)的同宿条件, 执行。特别地,许多边界曲线识别同斜切线并显示出在曲线上方存在同斜轨道,但是在其下方未获得同斜轨道。此外,相关的庞加莱图(通过Runge-Kutta-Gill仿真获得)证实了从这些图预测的同斜度条件是正确的。最后,使用计算机仿真来获得从很小的正弦外力观察到的实际混沌吸引子。这恰好与pt.I中报道的实验结果相对应,即从pt.I中的实际实验中观察到的混沌现象的确是基于同宿轨道的马蹄形混沌。

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