The Effect of Explosive Divergence in a Coupled Map Lattice of Matrices

Lu, Gang; Smidtaite, Rasa; Navickas, Zenonas; Ragulskis, Minvydas

doi:10.1016/j.chaos.2018.06.016

Cited by 10 publications

(6 citation statements)

References 33 publications

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“…Higher-order derivatives of the logistic mapping function vanish because it is a second-order polynomial. Te structure of coupled iterative maps represented by (14) becomes simpler compared to the general case in (12). Also, all perturbations at the nodes of the dot skeleton representation of the secret images are performed in terms of the auxiliary parameters.…”

Section: Discussionmentioning

confidence: 99%

“…CML was formally proposed by Kaneko in 1984 [1][2][3], where each node is coupled with its closest neighbors. Since then, many types of coupling were introduced [4][5][6][7][8][9][10][11][12][13]. A one-way coupling map lattice is used to derive a cryptosystem key generator in [4].…”

Section: Introductionmentioning

confidence: 99%

“…Te scheme of pseudorandom number generator combines the improved CML and time-varying delay in [11]. CML extensions when a scalar variable is replaced by a square matrix of variables are introduced in [12,13].…”

Section: Introductionmentioning

confidence: 99%

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Hyper Coupled Map Lattices for Hiding Multiple Images

et al. 2023

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The concept of a hyper coupled map lattice (CML) is presented in this paper. The complexity of the lattice is increased not by adding another spatial dimension of the lattice but by replacing scalar nodal variables by multidimensional square matrices of iterative variables. The proposed scheme exploits the nonlinear effects of the spatiotemporal divergence induced by nilpotent nodal matrices to generate separate secret images at different discrete moments of time during the evolution of the CML. The time variable plays the primary role in the decoding stage of the scheme. The carrying capacity of the proposed scheme is n − 1 different dichotomous digital images, where n is the dimension of the nilpotent nodal matrices. Computational experiments are used to demonstrate the efficacy of the proposed scheme.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hyper Coupled Map Lattices for Hiding Multiple Images

et al. 2023

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“…This fact has important implications for the study of discrete chaotic systems when the nodal complexity of the system is increased by expanding the dimension of the scalar variable [6][7][8][9]. Complex fractal patterns representing spatiotemporal divergence in the extended Kaneko model in [6], the development of a novel image hiding scheme in [7], spiral waves of divergence in [8], intermittent bursting in fractional logistic map in [9] are all based on divergence codes greater than zero. In other words, all these effects could not be observed if theorems 1 and 2 in [1] would hold true.…”

Section: Discussionmentioning

confidence: 99%

Commentary: Multidimensional discrete chaotic maps

Smidtaite

Ragulskis

2022

Front. Phys.

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This commentary is addressed to multidimensional discrete chaotic maps discussed in [1]. The authors of the commented paper [1] note that the iterative logistic map of matrices is introduced in [2, 3]. Then, the authors of [1] introduce a multidimensional discrete chaotic map, define when this map is explosive, and prove two theorems describing the conditions when the map is not explosive, and when a chaotic behavior is observed for each scalar variable.There are two issues commented in this commentary paper. The first one is related to the fact that multidimensional discrete chaotic maps have been already introduced in [4]. Secondly, both theorems describing the conditions when multidimensional discrete chaotic maps are not explosive, and when a chaotic behavior is observed for each scalar variable, do not hold true. Correct conditions when multidimensional discrete chaotic map is explosive are given in [2, 3] (for 2-dimensional discrete chaotic maps) and in [4] (for n-dimensional discrete chaotic maps). This commentary demonstrates that a multidimensional discrete chaotic map can be explosive even if the eigenvalues of the matrix of initial conditions are located in the convergence domain of the corresponding scalar discrete map. Necessary and sufficient conditions for a multidimensional discrete chaotic map to become explosive are discussed in [

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“…The CMLs are used in cryptography, physics, economics, steganography, and biology. They have a significant role in image encryption algorithms [ 44 , 45 , 46 ]. Then, we used a two-dimensional hyper-chaotic map CML to try pixel location.…”

Section: Methodsmentioning

confidence: 99%

A New Algorithm for Digital Image Encryption Based on Chaos Theory

Pourasad

Ranjbarzadeh

Mardani

2021

Entropy

140

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In recent decades, image encryption, as one of the significant information security fields, has attracted many researchers and scientists. However, several studies have been performed with different methods, and novel and useful algorithms have been suggested to improve secure image encryption schemes. Nowadays, chaotic methods have been found in diverse fields, such as the design of cryptosystems and image encryption. Chaotic methods-based digital image encryptions are a novel image encryption method. This technique uses random chaos sequences for encrypting images, and it is a highly-secured and fast method for image encryption. Limited accuracy is one of the disadvantages of this technique. This paper researches the chaos sequence and wavelet transform value to find gaps. Thus, a novel technique was proposed for digital image encryption and improved previous algorithms. The technique is run in MATLAB, and a comparison is made in terms of various performance metrics such as the Number of Pixels Change Rate (NPCR), Peak Signal to Noise Ratio (PSNR), Correlation coefficient, and Unified Average Changing Intensity (UACI). The simulation and theoretical analysis indicate the proposed scheme’s effectiveness and show that this technique is a suitable choice for actual image encryption.

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The Effect of Explosive Divergence in a Coupled Map Lattice of Matrices

Cited by 10 publications

References 33 publications

Hyper Coupled Map Lattices for Hiding Multiple Images

Hyper Coupled Map Lattices for Hiding Multiple Images

Commentary: Multidimensional discrete chaotic maps

A New Algorithm for Digital Image Encryption Based on Chaos Theory

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