Solution and dynamics of a fractional-order 5-D hyperchaotic system with four wings

Zhang, Limin; Sun, Kehui; He, Shaobo; Wang, Huihai; Xu, Yixin

doi:10.1140/epjp/i2017-11310-7

Cited by 66 publications

(27 citation statements)

References 29 publications

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“…is the initial value condition of the system, and J q t0 = (t−t0) q Γ(q+1) represent the integral operator of order q. The properties of the integral operator J q t0 are as follows [45]:…”

Section: B Adomian Decomposition Methodsmentioning

confidence: 99%

Color Image Compression-Encryption Using Fractional-Order Hyperchaotic System and DNA Coding

et al. 2020

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Recently, many encryption algorithms based on fractional-order chaotic system have been proposed to solve the problem of image encryption. In this paper, we propose a novel color image compression-encryption algorithm based on fractional-order hyperchaotic system and DNA coding. In the data compression stage, the data of R, G, and B channels of the color image are converted to the frequency domain by two-dimensional discrete cosine transform (DCT), and then the amount of encrypted data is reduced by the quantization process. We design a data processing algorithm to ensure that the data after DCT is compatible with DNA coding data format. In the encryption stage, the processes of DNA encoding and decoding, DNA operation, and pixel scrambling are all controlled by the corresponding chaotic sequences, which are generated by the chaotic system. The original image is used to calculate the initial state of the chaotic system, which improves the performance of the algorithm against the chosen-plaintext attack significantly. Experimental results and security analysis illustrate that the proposed algorithm has excellent compression and security performance. It can not only reconstruct the original image well under the condition of low compression ratio, but also provide high security to resist various attacks. Besides, experimental results also indicate that the algorithm proposed can be applied to the fields of color image compression, encryption, and transmission. INDEX TERMS Color image encryption, DNA encoding, fractional-order hyperchaotic system, discrete cosine transform(DCT), image compression.

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Section: B Adomian Decomposition Methodsmentioning

confidence: 99%

Color Image Compression-Encryption Using Fractional-Order Hyperchaotic System and DNA Coding

et al. 2020

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“…At present, research on 1D chaos, such as Logistic mapping [ 5 , 6 , 7 ]; 2D chaos, such as Henon mapping [ 8 , 9 , 10 ]; and 3D chaos, such as Rossler chaotic attractor [ 11 , 12 , 13 ], Chua [ 14 , 15 , 16 ], and Chen [ 17 , 18 , 19 ], have been very extensive and mature. With the development of chaos theory, many people began to study high-dimensional chaotic attractors, such as 4D chaotic attractor subsystems [ 20 , 21 , 22 , 23 ], 5D chaotic attractor subsystems [ 24 , 25 , 26 , 27 ], and 6D chaotic attractor subsystems [ 28 ]. In recent years, fractional-order chaotic systems [ 29 , 30 , 31 ], hidden attractors [ 32 , 33 , 34 ], and chaotic systems with co-existing attractors [ 35 , 36 ] have also been extensively studied.…”

Section: Introductionmentioning

confidence: 99%

The Establishment and Dynamic Properties of a New 4D Hyperchaotic System with Its Application and Statistical Tests in Gray Images

Ding

2020

Entropy

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In this paper, a new 4D hyperchaotic system is generated. The dynamic properties of attractor phase space, local stability, poincare section, periodic attractor, quasi-periodic attractor, chaotic attractor, bifurcation diagram, and Lyapunov index are analyzed. The hyperchaotic system is normalized and binary serialized, and the binary hyperchaotic stream generated by the system is statistically tested and entropy analyzed. Finally, the hyperchaotic binary stream is applied to the gray image encryption. The histogram, correlation coefficient, entropy test, and security analysis show that the hyperchaotic system has good random characteristics and can be applied to the gray image encryption.

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“…Chaotic flows with a plane of equilibria [9], without equilibria [10], with circular equilibria [11], with a line of equilibria [12], and with a stable equilibrium [13], are some examples. Understanding fractional-order chaotic systems is more challenging [14,15]. The control of integer and fractional-order chaotic systems has been a hot topic [16,17].…”

Section: Introductionmentioning

confidence: 99%

Investigation of Early Warning Indexes in a Three-Dimensional Chaotic System with Zero Eigenvalues

Chen

Nazarimehr

Jafari

et al. 2020

Entropy

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A rare three-dimensional chaotic system with all eigenvalues equal to zero is proposed, and its dynamical properties are investigated. The chaotic system has one equilibrium point at the origin. Numerical analysis shows that the equilibrium point is unstable. Bifurcation analysis of the system shows various dynamics in a period-doubling route to chaos. We highlight that from the evaluation of the entropy, bifurcation points can be predicted by identifying early warning signals. In this manner, bifurcation points of the system are analyzed using Shannon and Kolmogorov-Sinai entropy. The results are compared with Lyapunov exponents.

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Solution and dynamics of a fractional-order 5-D hyperchaotic system with four wings

Cited by 66 publications

References 29 publications

Color Image Compression-Encryption Using Fractional-Order Hyperchaotic System and DNA Coding

Color Image Compression-Encryption Using Fractional-Order Hyperchaotic System and DNA Coding

The Establishment and Dynamic Properties of a New 4D Hyperchaotic System with Its Application and Statistical Tests in Gray Images

Investigation of Early Warning Indexes in a Three-Dimensional Chaotic System with Zero Eigenvalues

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