The Lorenz chaotic system, statistical independence and sampling frequency

Dinu, Alexandru; Frunzete, Madalin

doi:10.1109/isscs52333.2021.9497431

Cited by 3 publications

(1 citation statement)

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“…The Lorenz system can be analyzed in multiple ways. The statistical investigations [20] on such a system have to take into consideration the proper implementation.…”

Section: Lorenz Systemmentioning

confidence: 99%

Quality Evaluation for Reconstructing Chaotic Attractors

Frunzete

2022

Mathematics

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Dynamical systems are used in various applications, and their simulation is related with the type of mathematical operations used in their construction. The quality of the system is evaluated in terms of reconstructing the system, starting from its final point to the beginning (initial conditions). Deciphering a message has to be without loss, and this paper will serve to choose the proper dynamical system to be used in chaos-based cryptography. The characterization of the chaotic attractors is the most important information in order to obtain the desired behavior. Here, observability and singularity are the main notions to be used for introducing an original term: quality observability index (q.o.i.). This is an original contribution for measuring the quality of the chaotic attractors. In this paper, the q.o.i. is defined and computed in order to confirm its usability.

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“…The Lorenz system can be analyzed in multiple ways. The statistical investigations [20] on such a system have to take into consideration the proper implementation.…”

Section: Lorenz Systemmentioning

confidence: 99%

Quality Evaluation for Reconstructing Chaotic Attractors

Frunzete

2022

Mathematics

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Random Number Generator Based on Optimization and Chaotic System

Yildirim

Tanyıldızı

2023

2023 11th International Symposium on Digital Forensics and Security (ISDFS)

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

Dinu

Frunzete

2023

Mathematics

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

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The Lorenz chaotic system, statistical independence and sampling frequency

Cited by 3 publications

References 4 publications

Quality Evaluation for Reconstructing Chaotic Attractors

Quality Evaluation for Reconstructing Chaotic Attractors

Random Number Generator Based on Optimization and Chaotic System

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

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