Discrete chaotic maps are a mathematical basis for many useful applications. One of the most common is chaos-based pseudorandom number generators (PRNGs), which should be computationally cheap and controllable and possess necessary statistical properties, such as mixing and diffusion. However, chaotic PRNGs have several known shortcomings, e.g., being prone to chaos degeneration, falling in short periods, and having a relatively narrow parameter range. Therefore, it is reasonable to design novel simple chaotic maps to overcome these drawbacks. In this study, we propose a novel fractal chaotic tent map, which is a generalization of the well-known tent map with a fractal function introduced into the right-hand side. We construct and investigate a PRNG based on the proposed map, showing its high level of randomness by applying the NIST statistical test suite. The application of the proposed PRNG to the task of generating surrogate data and a surrogate testing procedure is shown. The experimental results demonstrate that our approach possesses superior accuracy in surrogate testing across three distinct signal types—linear, chaotic, and biological signals—compared to the MATLAB built-in randn() function and PRNGs based on the logistic map and the conventional tent map. Along with surrogate testing, the proposed fractal tent map can be efficiently used in chaos-based communications and data encryption tasks.

The application of deep learning neural networks enables the processing of extensive volumes of data and often requires dense datasets. In certain domains, researchers encounter challenges related to the scarcity of training data, particularly in marine biology. In addition, many sounds produced by sea mammals are of interest in technical applications, e.g., underwater communication or sonar construction. Thus, generating synthetic biological sounds is an important task for understanding and studying the behavior of various animal species, especially large sea mammals, which demonstrate complex social behavior and can use hydrolocation to navigate underwater. This study is devoted to generating sperm whale vocalizations using a limited sperm whale click dataset. Our approach utilizes an augmentation technique predicated on the transformation of audio sample spectrograms, followed by the employment of the generative adversarial network StyleGAN2-ADA to generate new audio data. The results show that using the chosen augmentation method, namely mixing along the time axis, makes it possible to create fairly similar clicks of sperm whales with a maximum deviation of 2%. The generation of new clicks was reproduced on datasets using selected augmentation approaches with two neural networks: StyleGAN2-ADA and WaveGan. StyleGAN2-ADA, trained on an augmented dataset using the axis mixing approach, showed better results compared to WaveGAN.