Some chaotic properties of 2-𝒟 rational discrete map

AL-Yaseen, May Alaa Abdul-Khaleq; Zghair, Hayder Kadhim

doi:10.1080/09720502.2020.1790744

Cited by 1 publication

(2 citation statements)

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“…It is widely applied in information technology, electronic engineering, and various other fields, due to its boundedness initial value sensitivity, and inherent randomness. Researchers start to discover chaotic have more complex dynamical behaviors to make chaotic information encryption and chaotic secure communication more secure [11]- [14]. Zhou et al [15] designed a smooth quadratic 4-D autonomous hyperchaotic system having complex dynamical behavior, then analyzed Hopf bifurcation, Pitchfork bifurcation, the stability of the system and other dynamical problems by applying the central manifold theory and bifurcation theory.…”

Section: Introductionmentioning

confidence: 99%

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Image scrambler based on novel 4-D hyperchaotic system and magic square with fast Walsh–Hadamard transform

2022

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A novel 4-D hyperchaotic system that have seven positive parameters in third order with thirteen terms is proposed,in this paper, the proposed chaotic behavior is proved by analysis of the Lyapunov's exponent, fractional dimension, zero-one test, sensitivity dependent on initial condition (SDIC), phase portraits, and waveform analysis, this study offers an innovative designed image encryption algorithm depending on a 4-D chaotic system using fast discrete Walsh-Hadamard transform and magic matrix that is both effective and simple for image encryption and gives it a higher level of security. This new 4-D hyperchaotic system is used to produce a random key in this algorithm. The implemented and simulated results using mathematica programs and MATLAB programs were supplied qualitatively and in figures. The proposed system is hyperchaotic, according to testing results, because it possesses two Lyapunov positive exponents.

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Section: Introductionmentioning

confidence: 99%

“…Waveform analysis: proved that the waveforms are aperiodic, and waveform's time domain has noncyclical properties [11], [12]. Figure 3…”

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confidence: 99%