Logistic map: A possible random-number generator
Open accessAbstract
The logistic map is one of the simple systems exhibiting order to chaos transition. In this work we have investigated the possibility of using the logistic map in the chaotic regime (logmap) for a pseudorandom-number generator. To this end we have performed certain statistical tests on the series of numbers obtained from the logmap. We find that the logmap passes these tests satisfactorily and therefore it possesses many properties required of a pseudorandom-number generator.
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Chaotic behavior of the logistic map is observed only when the control parameter r is within the range (3.56995, 4).
“However, chaotic behavior is observed only when the control parameter, r, is within the range of (3.56995, 4) [19].”
From Image Encryption Algorithms: A Survey of Design and Evaluation Metrics (2024) · cites this paper as [19]
The Logistic Map (p. 4) explicitly states that the logistic map is chaotic at µ = 4. The claimed open interval (3.56995, 4) excludes 4, so the source contradicts the word “only.” (LLM, conf=0.90)
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Image Encryption Algorithms: A Survey of Design and Evaluation Metrics
Alghamdi, Y., & Munir, A. (2024) · Journal of Cybersecurity and Privacy · doi:10.3390/jcp4010007 · Cited by 98 · see citing works
“However, chaotic behavior is observed only when the control parameter, r , is within the range of (3.56995, 4) [19].”
BackgroundInfluential
- Authors
- Phatak, S. C., & Rao, S. S.
- Affiliations
- Institute of Physics, Bhubaneshwar (IN)
- ORCID
- Rao, S. Suresh
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 1995-04-01
- Volume
- 51
- Issue
- 4
- Pages
- 3670-3678
- ISSN
- 1063-651X (ISSN-L)
- 1095-3787
- OpenAlex
- W2165983133
- Cited by
- 233
- References
- 12
- Citations by year
- 2026: 13 · 2025: 17 · 2024: 13 · 2023: 18 · 2022: 20 · 2021: 14 · 2020: 17 · 2019: 13 · 2018: 9 · 2017: 9 · 2016: 8 · 2015: 7 · 2014: 12 · 2013: 7 · 2012: 7
- FWCI
- 0.55
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
- Keywords
- logistic map, pseudorandom number generators, chaotic dynamics, order-to-chaos transition, randomness testing, chaotic maps
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