Observation of Different Behaviors of Logistic Map for Different Control Parameters

Akter, Musammet Tahmina; Chowdhury, Mohammad Abul Mansur

doi:10.11648/j.ijamtp.20180403.14

Cited by 6 publications

(2 citation statements)

References 5 publications

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“…The logistic map is a simple mathematical model that plays a key role in chaos theory since it illustrates the emergence of chaotic behavior from a relatively simple nonlinear equation. It is often used as a prototype example to understand the dynamics of chaotic systems [59]. The logistic map time series x = {x 1 , x 2 , .…”

Section: Logistic Mapmentioning

confidence: 99%

Refined Composite Multiscale Fuzzy Dispersion Entropy and Its Applications to Bearing Fault Diagnosis

Rostaghi,

Khatibi,

Ashory

et al. 2023

Entropy

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Rotary machines often exhibit nonlinear behavior due to factors such as nonlinear stiffness, damping, friction, coupling effects, and defects. Consequently, their vibration signals display nonlinear characteristics. Entropy techniques prove to be effective in detecting these nonlinear dynamic characteristics. Recently, an approach called fuzzy dispersion entropy (DE–FDE) was introduced to quantify the uncertainty of time series. FDE, rooted in dispersion patterns and fuzzy set theory, addresses the sensitivity of DE to its parameters. However, FDE does not adequately account for the presence of multiple time scales inherent in signals. To address this limitation, the concept of multiscale fuzzy dispersion entropy (MFDE) was developed to capture the dynamical variability of time series across various scales of complexity. Compared to multiscale DE (MDE), MFDE exhibits reduced sensitivity to noise and higher stability. In order to enhance the stability of MFDE, we propose a refined composite MFDE (RCMFDE). In comparison with MFDE, MDE, and RCMDE, RCMFDE’s performance is assessed using synthetic signals and three real bearing datasets. The results consistently demonstrate the superiority of RCMFDE in detecting various patterns within synthetic and real bearing fault data. Importantly, classifiers built upon RCMFDE achieve notably high accuracy values for bearing fault diagnosis applications, outperforming classifiers based on refined composite multiscale dispersion and sample entropy methods.

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Section: Logistic Mapmentioning

confidence: 99%

Refined Composite Multiscale Fuzzy Dispersion Entropy and Its Applications to Bearing Fault Diagnosis

Rostaghi,

Khatibi,

Ashory

et al. 2023

Entropy

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“…The logistic map is used to forecast the new number of COVID-19 positive cases for selected countries. This is expressed mathematically as (Akter and Chowdhury, 2018) :…”

Section: Logistic Map Modelmentioning

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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Symmetric keys image encryption and decryption using 3D chaotic maps with DNA encoding technique

Patel

Bharath

2020

Multimed Tools Appl

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Observation of Different Behaviors of Logistic Map for Different Control Parameters

Cited by 6 publications

References 5 publications

Refined Composite Multiscale Fuzzy Dispersion Entropy and Its Applications to Bearing Fault Diagnosis

Refined Composite Multiscale Fuzzy Dispersion Entropy and Its Applications to Bearing Fault Diagnosis

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

Symmetric keys image encryption and decryption using 3D chaotic maps with DNA encoding technique

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