The Pattern Recognition System Using the Fractal Dimension of Chaos Theory

Shon, Young-Woo

doi:10.5391/ijfis.2015.15.2.121

Cited by 3 publications

(3 citation statements)

References 8 publications

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“…Aiming at the chaotic identification, scholars have proposed many criterions, such as Poincare section [4], bifurcation diagram [5], power spectrum [6], Kolmogorov entropy [7], and topological entropy [8]. The most commonly used criteria are the largest Lyapunov exponent [9,10] and the fractal dimension [11,12], but these two parameters are based on phase space reconstruction [13,14]. Only in real phase space or near-real phase space that the two parameters can accurately analyze and identify the signal.…”

Section: Introductionmentioning

confidence: 99%

A traffic data collection and analysis method based on wireless sensor network

Wang

Ouyang

Meng

et al. 2020

J Wireless Com Network

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With the rapid development of urbanization, collecting and analyzing traffic flow data are of great significance to build intelligent cities. The paper proposes a novel traffic data collection method based on wireless sensor network (WSN), which cannot only collect traffic flow data, but also record the speed and position of vehicles. On this basis, the paper proposes a data analysis method based on incremental noise addition for traffic flow data, which provides a criterion for chaotic identification. The method adds noise of different intensities to the signal incrementally by an improved surrogate data method and uses the delayed mutual information to measure the complexity of signals. Based on these steps, the trend of complexity change of mixed signal can be used to identify signal characteristics. The numerical experiments show that, based on incremental noise addition, the complexity trends of periodic data, random data, and chaotic data are different. The application of the method opens a new way for traffic flow data collection and analysis.

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Section: Introductionmentioning

confidence: 99%

A traffic data collection and analysis method based on wireless sensor network

Wang

Ouyang

Meng

et al. 2020

J Wireless Com Network

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“…Over the last few decades, the analysis and applications of chaotic dynamics in nonlinear systems have been widely studied in relation to various natural science disciplines including mathematics, chemistry, physics [ 1 , 2 ], and engineering [ 3 , 4 ]. However, many scholars and scientists have recently shown interest in applying these natural science models to social sciences [ 5 ] including areas such as psychology [ 6 ], family [ 7 ], addiction [ 8 , 9 , 10 , 11 , 12 ], happiness [ 13 , 14 , 15 , 16 ], and adult love and romantic relationships [ 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 ].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Chaotic Behavior in a Novel Extended Love Model Considering Positive and Negative External Environment

Huang

Bae

2018

Entropy

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Abstract:The aim of this study was to describe a novel extended dynamical love model with the external environments of the love story of Romeo and Juliet. We used the sinusoidal function as external environments as it could represent the positive and negative characteristics of humans. We considered positive and negative advice from a third person. First, we applied the same amount of positive and negative advice. Second, the amount of positive advice was greater than that of negative advice. Third, the amount of positive advice was smaller than that of negative advice in an external environment. To verify the chaotic phenomena in the proposed extended dynamic love affair with external environments, we used time series, phase portraits, power spectrum, Poincare map, bifurcation diagram, and the maximal Lyapunov exponent. With a variation of parameter "a", we recognized that the novel extended dynamic love affairs with different three situations of external environments had chaotic behaviors. We showed 1, 2, 4 periodic motion, Rössler type attractor, and chaotic attractor when parameter "a" varied under the following conditions: the amount of positive advice = the amount of negative advice, the amount of positive advice > the amount of negative advice, and the amount of positive advice < the amount of negative advice.

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“…If the control is. 𝑈 = [𝑢 1 𝑢 2 0] 𝑇 , 𝑢 1 = −𝑘𝑥 , 𝑢 2 = −𝑘𝑦, 𝑈 = [0 𝑢 2 𝑢 3 ] 𝑇 , 𝑢 2 = −𝑘𝑦 , 𝑢 3 = −𝑘𝑧 𝑈 = [ 𝑢 1 𝑢 2 𝑢 3] 𝑇 , 𝑢 1 = −𝑘𝑥, 𝑢 2 = −𝑘y , 𝑢 3 = −𝑘𝑧 Proof : The system(1) and new control can be written in the form : [ 𝑥ẏ ż ̇] = [ −𝑎 𝑎𝑏 0 𝑐 − 𝑧 0 −𝑥 𝑦 𝑥 −𝑏 ] [ 𝑥 𝑦 𝑧 ] + [ − 𝑘𝑥 −𝑘𝑦 0] …(14)…”

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confidence: 99%

Application Methods of Linear Feedback Control on the Modified Lorenz 3D Chaotic System

Younis¹,

Al-Kateeb²

2020

Tikrit J. Pure Sci.

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In this paper we using a linear feedback control methods on the Lorenz modified 3D system. we used the dynamical analysis system to find critical points, eigenvalues, and for stability, the Jacobi matrix, to investigate some dynamical behaviors of the system to find stability regions of the system in all methods used to suppress the originally unstable behavior of this system. The necessary and sufficient condition for suppression of unstable behavior for this system is getting positive feedback coefficient. Theoretical analysis and numerical simulation proved that the results obtained.

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The Pattern Recognition System Using the Fractal Dimension of Chaos Theory

Cited by 3 publications

References 8 publications

A traffic data collection and analysis method based on wireless sensor network

A traffic data collection and analysis method based on wireless sensor network

Analysis of Chaotic Behavior in a Novel Extended Love Model Considering Positive and Negative External Environment

Application Methods of Linear Feedback Control on the Modified Lorenz 3D Chaotic System

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