Designing Hyperchaotic Systems With &lt;newline/&gt;Any Desired Number of Positive Lyapunov &lt;newline/&gt;Exponents via A Simple Model

Shen, Chaowen; Yu, Simin; Lü, Jinhu; Chen, Guanrong

doi:10.1109/tcsi.2014.2304655

Cited by 110 publications

(33 citation statements)

References 28 publications

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“…In these applications, more positive Lyapunov exponents are often desired, and it is interesting to design memristive circuits with any number of positive Lyapunov exponents like [50,51]. In addition, many real-world engineering systems (e.g., neural networks) are complex networks composed of subsystems with connections among them.…”

Section: Resultsmentioning

confidence: 99%

Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria

Zeng

2014

Nonlinear Dyn

167

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This paper studies a four-dimensional (4D) memristive system modified from the 3D chaotic system proposed by Lü and Chen. The new system keeps the symmetry and dissipativity of the original system and has an uncountable infinite number of stable and unstable equilibria. By varying the strength of the memristor, we find rich complex dynamics, such as limit cycles, torus, chaos, and hyperchaos, which can peacefully coexist with the stable equilibria. To explain such coexistence, we compute the unstable manifolds of the equilibria, find that the manifolds create a safe zone for the hyperchaotic attractor, and also find many heteroclinic orbits. To verify the existence of hyperchaos in the 4D memristive circuit, we carry out a computerassisted proof via a topological horseshoe with twodirectional expansions, as well as a circuit experiment on oscilloscope views.

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Section: Resultsmentioning

confidence: 99%

Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria

Zeng

2014

Nonlinear Dyn

167

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“…We design an anti-control dissipative chaotic system referred by Chen 16 and introduce the features of chaotic systems. We design an anti-control dissipative chaotic system referred by Chen 16 and introduce the features of chaotic systems.…”

Section: D Chaotic System Descriptionmentioning

confidence: 99%

Secure color image encryption algorithm based on chaotic signals and its FPGA realization

Yang

Huang

2018

Circuit Theory & Apps

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In this paper, we designed a three-dimensional chaotic system (3D chaotic system). The continuous-time chaotic system had already been transformed into discrete-time (DT) chaotic system by Euler method. The phase portrait of DT chaotic system had been implemented on an oscilloscope via Altera field programmable gate array (FPGA) DE2-115. A cryptographic system of RGB image security for 3D chaotic system was proposed. There are three features in the encryption system. First, we use the information of plaintext image to produce the initial conditions of chaotic system. Second, the image of the permutation process shuffles the position of pixels in the plaintext image among RGB channels separately. Third, in the diffusion process, the pixels information in the shuffled image had been concealed by the XOR operation. The 3D chaotic encryption system had been also implemented on Altera DE2-115. Then, the cipher image can be obtained through the FPGA and simulated the image by Matlab code.In the security analysis, such as histogram analysis, correlation coefficient analysis, information entropy analysis, differential attack analysis (NPCR and UACI) have been performed in this paper. Experimental results show that the proposed algorithm has better security in comparison with other algorithms.

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“…Due to the complex structure, MD chaotic systems have found an increasingly large amount of applications in image encryption schemes [9,23,30]. MD hyper-chaotic systems with more complex dynamical characteristics than general chaotic systems were investigated [12,18,22]. Image encryption schemes based on hyper-chaotic systems were suggested to overcome the drawbacks existing in the cryptosystems with general chaotic systems [5,8,10,15,24].…”

Section: Introductionmentioning

confidence: 99%

A new image cryptosystem based on 2D hyper-chaotic system

Yuan

Liu

Gong

et al. 2016

Multimed Tools Appl

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An efficient image encryption scheme is designed based on 2D hyper-chaotic system. Different from the traditional chaos-based image encryption schemes, the confusion and the diffusion procedures of the proposed scheme are interacted on each other. In the encryption process, the position of the present pixel is influenced by the last diffused one. Then the corresponding diffused pixel makes a difference in the next pixel. By contrast with the traditional chaos-based image cryptosystems, the proposed cryptosystem with the interacted structure is steadier and harder to decipher. In addition, 2D hyper-chaotic systems are employed in the quicker generation of chaotic sequences in comparison to high-dimensional hyper-chaotic systems. Simulation results verify the security and effectiveness of this scheme.

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Designing Hyperchaotic Systems With <newline/>Any Desired Number of Positive Lyapunov <newline/>Exponents via A Simple Model

Cited by 110 publications

References 28 publications

Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria

Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria

Secure color image encryption algorithm based on chaotic signals and its FPGA realization

A new image cryptosystem based on 2D hyper-chaotic system

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