Performance of Finite Precision on Discrete Chaotic Map Based on a Feedback Shift Register

Huang, Chunguang; Ding, Qun

doi:10.1155/2020/4676578

Cited by 4 publications

(3 citation statements)

References 29 publications

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“…Suppose 𝜙( j) is a time series data where j =1, ..., N is the number of data. Then, the following steps are performed (Gottwald and Laskar, 2016) :…”

Section: The 0-1 Testmentioning

confidence: 99%

Chaos Theory of 0-1 Test and Logistic Map in New Confirmed COVID-19 Cases

Yusof

Sapini

Az’hari³

et al. 2022

Sci.Technol.Indones

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This study aims to forecast the new number of positive cases of COVID-19 using the logistic map, where the presence of chaos is determined using the 0-1 Test. There are a small number of investigations on chaos utilizing the 0-1 Test and logistic map in the literature. This study provides a straightforward technique of forecasting and a current way of determining chaos. Information on new confirmed COVID-19 cases and population of ten countries involving China, Vietnam, Korea, Malaysia, Singapore, New Zealand, India, USA, Brazil, and Mexico for six months from January 20 to June 15, 2020, are selected as samples. The logistic map runs through three stages: data training, forecasting, and validation using the Mean Absolute Error method (MAE). The data training procedure is critical for determining the best growth rate, r, for the logistic map. In chaotic investigations of the 0-1 Test, there appears to be an inverse expectation toward a logistic map. The 0-1 Test in the data of new confirmed COVID-19 cases in all the selected countries reveals the presence of non-chaotic. This contrasts with the existence of chaos in the logistic map forecasts for the USA, Brazil, and Mexico. Regardless, the logistic map was found to be capable of forecasting new COVID-19 positive cases with low error instances. Beginning in the middle of May 2020, new COVID-19 positive cases are forecasted to be on the rise in the USA, Brazil, and Mexico.

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“…Suppose 𝜙( j) is a time series data where j =1, ..., N is the number of data. Then, the following steps are performed (Gottwald and Laskar, 2016) :…”

Section: The 0-1 Testmentioning

confidence: 99%

Chaos Theory of 0-1 Test and Logistic Map in New Confirmed COVID-19 Cases

Yusof

Sapini

Az’hari³

et al. 2022

Sci.Technol.Indones

View full text Add to dashboard Cite

show abstract

“…More importantly, the final effect of this scheme depends on the switching rule and the switching system to a great extent, such that it is difficult to guarantee universality. The fourth is the perturbation mechanism [ 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]. Liu and Lin [ 23 ] created perturbation chaotic systems to perturb state variables and system parameters with a logistic map.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Control of Digital Baker Map with Application to Pseudo-Random Number Generator

Shi

Deng

2021

Entropy

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Dynamical degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based cryptosystems. The existing solutions mainly focus on the compensation of dynamical properties rather than on the elimination of the inherent biases of chaotic systems. In this paper, a unidirectional hybrid control method is proposed to improve the dynamical properties and to eliminate the biases of digital chaotic maps. A continuous chaotic system is introduced to provide external feedback control of the given digital chaotic map. Three different control modes are investigated, and the influence of control parameter on the properties of the controlled system is discussed. The experimental results show that the proposed method can not only improve the dynamical degradation of the digital chaotic map but also make the controlled digital system produce outputs with desirable performances. Finally, a pseudorandom number generator (PRNG) is proposed. Statistical analysis shows that the PRNG has good randomness and almost ideal entropy values.

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“…The effect of this method largely depends on the rules of switching. The fifth type is perturbation [ 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ]. Perturbation refers to adding a slight disturbance to the system.…”

Section: Introductionmentioning

confidence: 99%

An Error Compensation Method for Improving the Properties of a Digital Henon Map Based on the Generalized Mean Value Theorem of Differentiation

Deng

Shi

2021

Entropy

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Continuous chaos may collapse in the digital world. This study proposes a method of error compensation for a two-dimensional digital system based on the generalized mean value theorem of differentiation that can restore the fundamental performance of chaotic systems. Different from other methods, the compensation sequence of our method comes from the chaotic system itself and can be applied to higher-dimensional digital chaotic systems. The experimental results show that the improved system is highly consistent with the real chaotic system, and it has excellent chaotic characteristics such as high complexity, randomness, and ergodicity.

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Performance of Finite Precision on Discrete Chaotic Map Based on a Feedback Shift Register

Cited by 4 publications

References 29 publications

Chaos Theory of 0-1 Test and Logistic Map in New Confirmed COVID-19 Cases

Chaos Theory of 0-1 Test and Logistic Map in New Confirmed COVID-19 Cases

Hybrid Control of Digital Baker Map with Application to Pseudo-Random Number Generator

An Error Compensation Method for Improving the Properties of a Digital Henon Map Based on the Generalized Mean Value Theorem of Differentiation

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