张弛振子中加周期序列标度常数的映象阶数不依赖性

Order Independence of Period-Adding Sequences Scaling Constants for a Map from a Relaxation Oscillator

在最简单的张弛振子中,通过实验研究了当描述振子的映象阶数不同时加周期序列标度常数的变化。实验表明:当映象阶数为3阶时,沿临界线或沿超临界区某条线的加周期序列标度常数都分别为β～2.0和7～3.0;当映象阶数理论上为无穷阶,实践上高于3阶时,在误差范围内,β和γ的值与3阶时相同。这就证实加周期序列标度常数只反映法瑞树的性质,与映象的性质无关。

The paper studies experimentally the change of the period-adding sequences scaling constants when the order of the map describing the system varies in a simplest relaxation oscillator. The results are: the constants along the eritical line and above it both are β～2.0 and γ～3.0 when the order of the map is three; in the case of the theoretical infinite and practically higher than three map orders, β and γ have the same values inside the error range, which certifies that the period-adding sequences scaling constants just reflect the properties of Farcy tree and are independent of the system's map.