Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems

He, Shaobo; Li, Chunbiao; Sun, Kehui; Jafari, Sajad

doi:10.3390/e20080556

Cited by 45 publications

(17 citation statements)

References 32 publications

(52 reference statements)

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“…Previous research has established that entropy is an effective index for estimating information in a particular system [ 21 , 22 , 23 ]. The authors applied entropy measurement to consider the complexity/chaos of dynamical systems [ 24 , 25 , 26 , 27 ]. In particular, approximate entropy (ApEn) [ 28 , 29 ] is useful to study chaotic systems [ 19 , 30 ].…”

Section: Chaotic Mapmentioning

confidence: 99%

Chaotic Map with No Fixed Points: Entropy, Implementation and Control

Khang

Ouannas

Wang

et al. 2019

Entropy

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A map without equilibrium has been proposed and studied in this paper. The proposed map has no fixed point and exhibits chaos. We have investigated its dynamics and shown its chaotic behavior using tools such as return map, bifurcation diagram and Lyapunov exponents' diagram. Entropy of this new map has been calculated. Using an open micro-controller platform, the map is implemented, and experimental observation is presented. In addition, two control schemes have been proposed to stabilize and synchronize the chaotic map.

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Section: Chaotic Mapmentioning

confidence: 99%

Chaotic Map with No Fixed Points: Entropy, Implementation and Control

Khang

Ouannas

Wang

et al. 2019

Entropy

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“…Among others, we have systems with extreme multistability (characterized by the coexistence of an infinite number of attractors, in this case, the bifurcation control parameter is one of the initial conditions) [ 27 – 30 ]. Other types of multistable systems found recently are systems with megastability [ 31 – 35 ]. These later cases have an infinite number of coexisting attractors, but there are no such bifurcations in them like systems with extreme multistability [ 32 ].…”

Section: Introductionmentioning

confidence: 99%

Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

Njitacke

Doubla

Tsafack

et al. 2020

Neural Comput & Applic

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In this contribution, the problem of multistability control in a simple model of 3D HNNs as well as its application to biomedical image encryption is addressed. The space magnetization is justified by the coexistence of up to six disconnected attractors including both chaotic and periodic. The linear augmentation method is successfully applied to control the multistable HNNs into a monostable network. The control of the coexisting four attractors including a pair of chaotic attractors and a pair of periodic attractors is made through three crises that enable the chaotic attractors to be metamorphosed in a monostable periodic attractor. Also, the control of six coexisting attractors (with two pairs of chaotic attractors and a pair of periodic one) is made through five crises enabling all the chaotic attractors to be metamorphosed in a monostable periodic attractor. Note that this controlled HNN is obtained for higher values of the coupling strength. These interesting results are obtained using nonlinear analysis tools such as the phase portraits, bifurcations diagrams, graph of maximum Lyapunov exponent, and basins of attraction. The obtained results have been perfectly supported using the PSPICE simulation environment. Finally, a simple encryption scheme is designed jointly using the sequences of the proposed HNNs and the sequences of real/imaginary values of the Julia fractals set. The obtained cryptosystem is validated using some well-known metrics. The proposed method achieved entropy of 7.9992, NPCR of 99.6299, and encryption time of 0.21 for the 256*256 sample 1 image.

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“…Different entropy measures have been proposed to study the complexity of chaotic attractors [ 39 ]. Chaotic dynamics and their complexities have been analyzed in [ 40 , 41 , 42 ]. Local entropy has been used for image segmentation in [ 43 ].…”

Section: Introductionmentioning

confidence: 99%

Entropy Analysis and Image Encryption Application Based on a New Chaotic System Crossing a Cylinder

Farhan

Al-Saidi

Maolood

et al. 2019

Entropy

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Designing chaotic systems with specific features is a hot topic in nonlinear dynamics. In this study, a novel chaotic system is presented with a unique feature of crossing inside and outside of a cylinder repeatedly. This new system is thoroughly analyzed by the help of the bifurcation diagram, Lyapunov exponents’ spectrum, and entropy measurement. Bifurcation analysis of the proposed system with two initiation methods reveals its multistability. As an engineering application, the system’s efficiency is tested in image encryption. The complexity of the chaotic attractor of the proposed system makes it a proper choice for encryption. States of the chaotic attractor are used to shuffle the rows and columns of the image, and then the shuffled image is XORed with the states of chaotic attractor. The unpredictability of the chaotic attractor makes the encryption method very safe. The performance of the encryption method is analyzed using the histogram, correlation coefficient, Shannon entropy, and encryption quality. The results show that the encryption method using the proposed chaotic system has reliable performance.

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Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems

Cited by 45 publications

References 32 publications

Chaotic Map with No Fixed Points: Entropy, Implementation and Control

Chaotic Map with No Fixed Points: Entropy, Implementation and Control

Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

Entropy Analysis and Image Encryption Application Based on a New Chaotic System Crossing a Cylinder

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