Clocking divergence of iterative maps of matrices

Smidtaite, Rasa; Navickas, Zenonas; Ragulskis, Minvydas

doi:10.1016/j.cnsns.2020.105589

Cited by 4 publications

(17 citation statements)

References 9 publications

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“…It can be noted that a scalar variable in Eq. 1 can be also replaced by the nth order square matrix [4]. However, it appears that the dynamics of n-dimensional discrete chaotic maps becomes much more complicated compared to the dynamics of 2-dimensional discrete chaotic maps [4].…”

Section: N-dimensional Discrete Chaotic Mapsmentioning

confidence: 99%

“…A multidimensional discrete chaotic map may become explosive if at least two eigenvalues of the matrix of initial conditions do coincide (even though all eigenvalues of the matrix are located in the convergence domain of the corresponding scalar discrete map). The multiplicity indexes of eigenvalues are directly related to the packing codes due to the classical bin packing problem [4]. Therefore, the study of packing codes becomes a topic of primary importance in the analysis of the divergence of multidimensional discrete chaotic maps [4].…”

Section: Packing and Divergence Codesmentioning

confidence: 99%

“…The multiplicity indexes of eigenvalues are directly related to the packing codes due to the classical bin packing problem [4]. Therefore, the study of packing codes becomes a topic of primary importance in the analysis of the divergence of multidimensional discrete chaotic maps [4]. Also, it is demonstrated in [4] that there exists a bijective correspondence between the packing and the divergence codes.…”

Section: Packing and Divergence Codesmentioning

confidence: 99%

“…Therefore, the study of packing codes becomes a topic of primary importance in the analysis of the divergence of multidimensional discrete chaotic maps [4]. Also, it is demonstrated in [4] that there exists a bijective correspondence between the packing and the divergence codes. On their turn, divergence codes define the rate of divergence of multidimensional discrete chaotic maps [4].…”

Section: Packing and Divergence Codesmentioning

confidence: 99%

“…Also, it is demonstrated in [4] that there exists a bijective correspondence between the packing and the divergence codes. On their turn, divergence codes define the rate of divergence of multidimensional discrete chaotic maps [4]. Let us illustrate the packing and the divergence codes for a 4-dimensional discrete chaotic map.…”

Section: Packing and Divergence Codesmentioning

confidence: 99%

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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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Section: N-dimensional Discrete Chaotic Mapsmentioning

confidence: 99%

Section: Packing and Divergence Codesmentioning

confidence: 99%

Section: Packing and Divergence Codesmentioning

confidence: 99%

Section: Packing and Divergence Codesmentioning

confidence: 99%

Section: Packing and Divergence Codesmentioning

confidence: 99%

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Commentary: Multidimensional discrete chaotic maps

Smidtaite

Ragulskis

2022

Front. Phys.

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Finite-time divergence in Chialvo hyperneuron model of nilpotent matrices

Smidtaite,

Ragulskis

2024

Chaos, Solitons & Fractals

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Intermittent Bursting in the Fractional Difference Logistic Map of Matrices

Petkevičiūtė-Gerlach

Smidtaite

Ragulskis

2022

Int. J. Bifurcation Chaos

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Intermittent bursting in the fractional difference logistic map of matrices is studied in this paper. Analytic relationships governing the dynamics of the fractional difference map of matrices are derived in an explicit form. Computational experiments are used to prove the existence of intermittent bursts located far away from the initial conditions. Such isolated waves of temporary divergence in the fractional difference logistic map of matrices are demonstrated for the first time. Intermittent bursts of temporary divergence offer new possibilities for designing advanced information hiding algorithms.

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Clocking divergence of iterative maps of matrices

Cited by 4 publications

References 9 publications

Commentary: Multidimensional discrete chaotic maps

Commentary: Multidimensional discrete chaotic maps

Finite-time divergence in Chialvo hyperneuron model of nilpotent matrices

Intermittent Bursting in the Fractional Difference Logistic Map of Matrices

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