Generation of Numbers with the Distribution Close to Uniform with the Use of Chaotic Maps

Lawnik, Marcin

doi:10.5220/0005090304510455

Cited by 9 publications

(5 citation statements)

References 12 publications

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“…It requires the knowledge of the frequency of the occurrence of particular branches of the transformation during the process of generating the uniform distribution described in [20]. However, neither the density function nor the cumulative distribution function are directly used in the method.…”

Section: Discussionmentioning

confidence: 99%

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Generation of pseudo-random numbers with the use of inverse chaotic transformation

Lawnik

2018

Open Mathematics

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In (Lawnik M., Generation of numbers with the distribution close to uniform with the use of chaotic maps, In: Obaidat M.S., Kacprzyk J., Ören T. (Ed.), International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH) (28-30 August 2014, Vienna, Austria), SCITEPRESS, 2014) Lawnik discussed a method of generating pseudo-random numbers from uniform distribution with the use of adequate chaotic transformation. The method enables the " attening" of continuous distributions to uniform one. In this paper a inverse process to the above-mentioned method is presented, and, in consequence, a new manner of generating pseudo-random numbers from a given continuous distribution. The method utilizes the frequency of the occurrence of successive branches of chaotic transformation in the process of " attening". To generate the values from the given distribution one discrete and one continuous value of a random variable are required. The presented method does not directly involve the knowledge of the density function or the cumulative distribution function, which is, undoubtedly, a great advantage in comparison with other well-known methods. The described method was analysed on the example of the standard normal distribution.

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Section: Discussionmentioning

confidence: 99%

“…As shown in [19], iterating (6) with parameter value a close to , generates values from the normal distribution. Another method which applies chaotic maps in pseudo-random numbers generation was shown in [20], where values from uniform distribution are generated. This method may be described by the following procedure: Method 1.…”

Section: Introductionmentioning

confidence: 99%

Generation of pseudo-random numbers with the use of inverse chaotic transformation

Lawnik

2018

Open Mathematics

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“…Another problem related to data, in particular large data sets, is their processing [40], including sorting [41][42][43], or processing to get random values from the collected data [44]. The proposed method of data storage allows for further processing, even though they are hidden to the human eye.…”

Section: Filementioning

confidence: 99%

A New Way to Store Simple Text Files

Lawnik¹,

Pełka²,

Kapczyński³

2020

Algorithms

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In the era of ubiquitous digitization, the Internet of Things (IoT), information plays a vital role. All types of data are collected, and some of this data are stored as text files. An important aspect—regardless of the type of data—is related to file storage, especially the amount of disk space that is required. The less space is used on storing data sets, the lower is the cost of this service. Another important aspect of storing data warehouses in the form of files is the cost of data transmission needed for file transfer and its processing. Moreover, the data that are stored should be minimally protected against access and reading by other entities. The aspects mentioned above are particularly important for large data sets like Big Data. Considering the above criteria, i.e., minimizing storage space, data transfer, ensuring minimum security, the main goal of the article was to show the new way of storing text files. This article presents a method that converts data from text files like txt, json, html, py to images (image files) in png format. Taking into account such criteria as the output size of the file, the results obtained for the test files confirm that presented method enables to reduce the need for disk space, as well as to hide data in an image file. The described method can be used for texts saved in extended ASCII and UTF-8 coding.

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“…In nature, chaos is a nonlinear phenomena of nonlinear dynamical systems which is unpredictable, aperiodic and extreme sensitive on initial values [1,2]. There is diversity of fields in which chaotic maps and fractals are widely studied [3,4,5,6,7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

On the Complex and Chaotic Dynamics of Standard Logistic Sine Square Map

Kumari

Chugh

Miculescu

2021

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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In this article, we set up a new nonlinear dynamical system which is derived by combining logistic map and sine square map in Mann orbit (a two step feedback process) for ameliorating the stability performance of chaotic system and name it Standard Logistic Sine Square Map (SLSSM). The purpose of this paper is to study the whole dynamical behavior of the proposed map (SLSSM) through various introduced aspects consisting fixed point and stability analysis, time series representation, bifurcation diagram and Lyapunov exponent. Moreover, we show that our map is significantly superior than existing other one dimensional maps. We investigate that the chaotic and complex behavior of SLSSM can be controlled by selecting control parameters carefully. Also, the range of convergence and stability can be made to increase drastically. This new system (SLSSM) might be used to achieve better results in cryptography and to study chaos synchronization.

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Generation of Numbers with the Distribution Close to Uniform with the Use of Chaotic Maps

Cited by 9 publications

References 12 publications

Generation of pseudo-random numbers with the use of inverse chaotic transformation

Generation of pseudo-random numbers with the use of inverse chaotic transformation

A New Way to Store Simple Text Files

On the Complex and Chaotic Dynamics of Standard Logistic Sine Square Map

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