The aperiodic stochastic resonance (ASR) in the bistable fractional-order system is further studied when the fractional-order lies in the interval (0, 2). In previous works, the ASR can only process aperiodic binary signal with large pulse width. However, for the signal with small pulse width, the method cannot work. Actually, the signals with small pulse width are also common in the information transmission field. It greatly limits the application of the fractional stochastic resonance. Hence, we mainly focus on the enhancement of aperiodic binary signal with small pulse width. To solve the aforementioned technical problem, the general scale transformation is introduced, which allows us to achieve the ASR successfully. By this method, the equivalent system with large system parameters is able to match the input character signal with arbitrary small pulse width well, where the scale parameter is a key to achieve resonance. During the process, the fractional-order system presents rich dynamical behaviors in processing the aperiodic binary signals. Especially, as the order increases, the output signal at optimal noise intensity might be better and be more similar to the input one. This indicates the fractional order can optimize the stochastic resonance. The results might provide some reference to the engineering field, such as digital transmission and image processing field.

中文翻译：

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分数阶双稳态系统中的非周期随机共振

当分数阶位于区间（0, 2）时，进一步研究了双稳态分数阶系统中的非周期随机共振（ASR）。在以前的工作中，ASR 只能处理大脉冲宽度的非周期性二进制信号。但是，对于脉宽小的信号，该方法是行不通的。实际上，小脉冲宽度的信号在信息传输领域也很常见。它极大地限制了分数随机共振的应用。因此，我们主要关注小脉冲宽度的非周期性二进制信号的增强。为了解决上述技术问题，引入了通用的尺度变换，这使得我们能够成功地实现ASR。通过这种方法，大系统参数的等效系统能够很好地匹配任意小脉冲宽度的输入字符信号，其中尺度参数是实现谐振的关键。在此过程中，分数阶系统在处理非周期性二进制信号时表现出丰富的动力学行为。特别是，随着阶数的增加，最佳噪声强度的输出信号可能会更好，并且与输入信号更相似。这表明分数阶可以优化随机共振。研究结果可为数字传输、图像处理等工程领域提供一定的参考。特别是，随着阶数的增加，最佳噪声强度的输出信号可能会更好，并且与输入信号更相似。这表明分数阶可以优化随机共振。研究结果可为数字传输、图像处理等工程领域提供一定的参考。特别是，随着阶数的增加，最佳噪声强度的输出信号可能会更好，并且与输入信号更相似。这表明分数阶可以优化随机共振。研究结果可为数字传输、图像处理等工程领域提供一定的参考。