| Full text | |
| Author(s): |
Valle, Joao
;
Bruno, Odemir M.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | CHAOS SOLITONS & FRACTALS; v. 180, p. 9-pg., 2024-01-24. |
| Abstract | |
Among the dynamics that the logistic map orbit can present, the chaotic behavior is highlighted due to its complexity. Despite extensive research on this type of dynamics, chaotic systems still exhibit divergence between analytical and numerical behavior due to the numerical precision limitations of computers. This limitation significantly impacts research on chaotic systems using a numerical approach. To address this issue, methods have been developed to compute the last digits of infinite -arithmetic precision orbits of the logistic map. As a result, fixed and periodic dynamics are found in the last digits of real logistic map orbits. Despite the evidence of such digits, their dynamic properties have not been extensively explored. This paper analyzed the stability, attraction, and classes of the fixed digits, as well as the stability dependency and frequency properties of periodic digits. Among the results are fixed digits with stable and unstable behavior, as well as the phenomenon of attraction. Additionally, frequency in the digits was found in the cycles generated by the periodic digits, along with a dependency relationship with the fixed digits exhibiting stable behavior. Our results reveal a diversity of properties and dynamics in the least significant digits of analytical logistic map orbits. (AU) | |
| FAPESP's process: | 21/08325-2 - An analysis of network automata as models for biological and natural processes |
| Grantee: | Odemir Martinez Bruno |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 22/01935-2 - Patterns and pseudorandomness in iterative maps in a chaotic regime |
| Grantee: | João Pedro do Valle Alvarenga |
| Support Opportunities: | Scholarships in Brazil - Master |
| FAPESP's process: | 18/22214-6 - Towards a convergence of technologies: from sensing and biosensing to information visualization and machine learning for data analysis in clinical diagnosis |
| Grantee: | Osvaldo Novais de Oliveira Junior |
| Support Opportunities: | Research Projects - Thematic Grants |