Book of Abstracts for 2nd International Conference on Mathematical Modelling in Mechanics and Engineering, Belgrade.
ISSN/ISBN: 978-86-80593-77-7 DOI: Not available at this time.
Abstract: Benford’s law, also known as a first digit law, gives a monotonically decreasing distribution of the first digit in the considered data set. In a contradiction with our intuition of appearing of first digit with uniform distribution, this is decreasingly logarithmic law, where the digit 1 is appearing with 30% chance and the digit 9 is appearing with 4.58% chance. It is expected that data, such as: the sizes of events, populations of cities, the flow rates of rivers, the sizes of heavenly bodies, market values, companies’ revenues, daily trading volumes follow Benford’s law. Also, there are some limitations of the law application, like: coded data, the numbers used as identification numbers, psychologically rounded numbers or natural bounded data with minimum or maximum. The law is also a test of the diversity of data and gives an answer on the question of possible manipulation of the data. The purpose of this paper is to consider does the Benford’s law can be applied on different dynamical systems. These dynamical systems have been employed to describe the broad range of applications in the natural and social sciences, like in mathematics, chemistry, physics, engineering, economics, etc. They are fundamental part of chaos theory and the edge of chaos concept, logistic map dynamics, bifurcation theory, the self-assembly and self-organization processes. As a procedure, we analyze the frequency of the first digit of the coordinates of the trajectories generated by some dynamical systems. We conclude that some trajectories follow Benford’s law, some don’t follow the law, and some results depend of the choise of the parameters of the model. As the main point is that natural data will follow Benford’s law, and we have shown that for the some dynamical systems the distinction between the trajectories that follow Benford’s law and that do not follow Benford’s law may be very small. Conclusion is that the application of Benford’s law in order to make a difference between “natural” data and “artificial” data may require much more careful consideration.
Bibtex:
@inproceedings{,
AUTHOR={Vesna Rajić and Jelena Stanojević and Nataša Trišović},
TITLE={Benford’s Law with Application in Dynamical Systems},
BOOKTITLE={Book of Abstracts for 2nd International Conference on Mathematical Modelling in Mechanics and Engineering},
ADDRESS={Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade},
MONTH={September},
YEAR={2024},
URL={http://repo.pw.edu.pl/info/book/WUT0237c1ae327747f0bf13b4b630f67a24/},
}
Reference Type: Conference Paper
Subject Area(s): Dynamical Systems