Complicated, but rational, phase-locking responses of an ideal time-base oscillator
Complicated, but rational, phase-locking responses of an ideal time-base oscillator
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理想时基振荡器的复杂但合理的锁相响应
DOI：
10.1109/tcs.1983.1085410
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发表时间：
1983
期刊：
影响因子：
--
通讯作者：
T. Allen
中科院分区：
文献类型：
--
作者：
T. Allen
提出了一个模型来解释由一系列激励脉冲驱动的原型时基振荡器的复杂锁相响应。该模型预测不同锁相比的稳定区间应作为参数的函数出现在特定序列中。对于一个参数（耦合强度）的变化，这些序列包括固定参数（固有频率比）的简单连分数的奇数收敛和相关联的半收敛。关于第二参数的变化，序列包括先前未描述的算术级数，其与Farey级数密切相关。描述了该模型的实验测试。结果大体上是证实性的。然而，参数空间上存在狭窄的区间，其中伪随机性与真实噪声的影响是一个未解决的问题。
A model is advanced to account for the complicated phase-locking responses of a prototypical time-base oscillator driven by a train of excitory pulses. The model predicts that the intervals of stability for different ratios of phase locking should occur in specific sequences as functions of the parameters. With respect to variation of one parameter (a strength of coupling), these sequences comprise the odd convergents and associated semiconvergents of the simple continued fraction for the fixed parameter (a natural frequency ratio). With respect to variation of this second parameter, the sequences comprise a previously undescribed arithmetical series, which is closely related to the Farey series. An experimental test of the model is described. The results are by and large confirmatory. However, there are narrow intervals on the parameter space where pseudo-randomness versus the effects of true noise are an unresolved issue.