A simple jerk system with only one exponential nonlinearity is proposed and discussed. Dynamic analysis of the integer-order jerk system shows the existence of chaotic oscillations. A model for the fractional-order jerk system is derived. The Adomian decomposition method is used to analyse the fractional-order jerk system. Stability analysis of the fractional-order jerk system shows that chaotic oscillations exist in orders less than one and bifurcation analysis shows the range of fractional orders for periodic and chaotic oscillations. To show the randomness of the fractional-order jerk system, a pseudorandom number generator is designed and tested. The NIST-800-22 tests show that the proposed fractional-order jerk system is effective in showing randomness. Finally, an image hiding application to the audio data has been realized by using the developed RNG algorithm. The encrypted image is hidden by being embedded in the audio data, and then, on the receiver side, the data are recovered by taking the image data from the hidden audio file.

提出并讨论了一个只有一个指数非线性的简单的混蛋系统。整数阶冲击系统的动态分析表明存在混沌振荡。推导了分数阶冲击系统的模型。Adomian分解方法用于分析分数阶加加速度系统。分数阶冲击系统的稳定性分析表明，混沌振荡的阶次小于1，而分叉分析表明分数阶振荡的范围为周期性和混沌振荡。为了显示分数阶加加速度系统的随机性，设计并测试了伪随机数生成器。NIST-800-22测试表明，提出的分数阶加扰系统可有效显示随机性。最后，通过使用开发的RNG算法，已经实现了对音频数据的图像隐藏应用程序。通过将加密的图像嵌入音频数据中来隐藏该图像，然后在接收方，通过从隐藏的音频文件中获取图像数据来恢复数据。