This report presents rigorous analysis of Arnol'd tongues generated by a manifold piecewise linear circuit. The circuit comprises an LC oscillator, a conductive switch that produces the manifold, and a voltage source controlled by the current value through the inductor when the voltage across the capacitor exceeds a threshold. From the circuit dynamics, the Poincaré return map is explicitly derived as a piecewise linear circle map, and the generation of Arnol'd tongues is precisely explained. We attempt to derive the border–collision bifurcation boundaries of the Arnol'd tongues, some of which are obtained explicitly. Furthermore, we experimentally verify these theoretical results. © 2020 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

中文翻译：

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从歧管分段线性电路严格分析Arnol舌头

该报告对由歧管分段线性电路产生的Arnol舌头进行了严格的分析。该电路包括一个LC振荡器，一个产生歧管的导电开关，以及一个在电容器两端的电压超过阈值时受通过电感器的电流值控制的电压源。从电路动力学来看，庞加莱返回映射明确地导出为分段线性圆映射，并且精确解释了Arnol'd舌的生成。我们尝试导出Arnol'd舌的边界-碰撞分叉边界，其中一些是明确获得的。此外，我们通过实验验证了这些理论结果。©2020日本电气工程师学会。由John Wiley＆Sons，Inc.发布