Singularity, Observability and Statistical Independence in the Context of Chaotic Systems

Pseudorandom number generators (PRNGs) have always been a central research topic in data science, and chaotic dynamical systems are one of the means to obtain scientifically proven data. Chaotic property that they seemingly unpredictable random behavior obtained by making use deterministic laws. The current paper will show how several notions used study systems—statistical independence, singularity, observability—can be together as suite test methods for with high potential being PRNG or cryptography fields. In order address these topics, we relied on adaptation observability coefficient previous papers authors, calculated singularity areas considered, evaluated selected maps from statistical independence point view. By three above, managed find strong correlations between proposed, thus supporting idea resulting procedure is consistent. Future directions consist applying proposed other gather more formalize approach can scientist when selecting best system specific (PRNG, cryptography, etc.).