Design and Analysis of a Quadratic Lorenz-like Attractor for Pseudo-Random Number Generation

Bugce Eminaga Tatlicioglu; Hatice Aktöre

doi:10.17776/csj.1557049

EN

Design and Analysis of a Quadratic Lorenz-like Attractor for Pseudo-Random Number Generation

Abstract

This study introduces and analyzes a novel quadratic Lorenz-like attractor and demonstrates its application as a pseudo-random number generator (PRNG). A theoretical and numerical investigation of the system dynamics is conducted, including equilibrium point analysis, Jacobian eigenvalues, dissipativity, and Lyapunov exponents. The results indicate that the quadratic modification alters the system dynamics, producing stronger chaotic intensity than the classical Lorenz system. This is supported by larger positive Lyapunov exponents and a non-integer Lyapunov dimension (≈2.40), which reflects a more complex attractor geometry. Numerical simulations, time series, phase projections, and bifurcation analysis further illustrate the rich nonlinear dynamics of the system. To validate its applicability, the chaotic sequences generated by the attractor were subjected to standard statistical evaluations, including the NIST SP800-22, Diehard, and ENT test suites. A dataset of 18 million samples was employed, significantly exceeding the minimum requirement for meaningful validation, and the results confirm that the proposed generator produces high-quality randomness. The importance of this work lies in demonstrating that the quadratic Lorenz-like attractor offers both strong chaotic intensity and relatively simple structure, making it a promising candidate for cryptographic applications, secure communications, and other domains requiring reliable pseudo-random number generation.

Keywords

Chaos Theory, Random number generation, Dynamical system, Lorenz attractor

Ethical Statement

no ethıcal

References

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Details

Primary Language

English

Subjects

Dynamical Systems in Applications, Applied Mathematics (Other)

Journal Section

Research Article

Authors

Bugce Eminaga Tatlicioglu ^*
0000-0001-8854-4464
Cyprus

Hatice Aktöre
0000-0003-2455-3681
Cyprus

Publication Date

December 30, 2025

Submission Date

September 27, 2024

Acceptance Date

November 27, 2025

Published in Issue

Year 2025 Volume: 46 Number: 4

DOI

https://doi.org/10.17776/csj.1557049

IZ

https://izlik.org/JA67AC36WJ

APA

Eminaga Tatlicioglu, B., & Aktöre, H. (2025). Design and Analysis of a Quadratic Lorenz-like Attractor for Pseudo-Random Number Generation. Cumhuriyet Science Journal, 46(4), 891-901. https://doi.org/10.17776/csj.1557049

AMA

1.Eminaga Tatlicioglu B, Aktöre H. Design and Analysis of a Quadratic Lorenz-like Attractor for Pseudo-Random Number Generation. CSJ. 2025;46(4):891-901. doi:10.17776/csj.1557049

Chicago

Eminaga Tatlicioglu, Bugce, and Hatice Aktöre. 2025. “Design and Analysis of a Quadratic Lorenz-Like Attractor for Pseudo-Random Number Generation”. Cumhuriyet Science Journal 46 (4): 891-901. https://doi.org/10.17776/csj.1557049.

EndNote

Eminaga Tatlicioglu B, Aktöre H (December 1, 2025) Design and Analysis of a Quadratic Lorenz-like Attractor for Pseudo-Random Number Generation. Cumhuriyet Science Journal 46 4 891–901.

IEEE

[1]B. Eminaga Tatlicioglu and H. Aktöre, “Design and Analysis of a Quadratic Lorenz-like Attractor for Pseudo-Random Number Generation”, CSJ, vol. 46, no. 4, pp. 891–901, Dec. 2025, doi: 10.17776/csj.1557049.

ISNAD

Eminaga Tatlicioglu, Bugce - Aktöre, Hatice. “Design and Analysis of a Quadratic Lorenz-Like Attractor for Pseudo-Random Number Generation”. Cumhuriyet Science Journal 46/4 (December 1, 2025): 891-901. https://doi.org/10.17776/csj.1557049.

JAMA

1.Eminaga Tatlicioglu B, Aktöre H. Design and Analysis of a Quadratic Lorenz-like Attractor for Pseudo-Random Number Generation. CSJ. 2025;46:891–901.

MLA

Eminaga Tatlicioglu, Bugce, and Hatice Aktöre. “Design and Analysis of a Quadratic Lorenz-Like Attractor for Pseudo-Random Number Generation”. Cumhuriyet Science Journal, vol. 46, no. 4, Dec. 2025, pp. 891-0, doi:10.17776/csj.1557049.

Vancouver

1.Bugce Eminaga Tatlicioglu, Hatice Aktöre. Design and Analysis of a Quadratic Lorenz-like Attractor for Pseudo-Random Number Generation. CSJ. 2025 Dec. 1;46(4):891-90. doi:10.17776/csj.1557049

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December

Abstract

Design and Analysis of a Quadratic Lorenz-like Attractor for Pseudo-Random Number Generation

Abstract

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