Modeling methods and characteristic analysis of new Hamiltonian and non-Hamiltonian conservative chaotic systems

Leng, Xiangxin; Zhang, Chenkai; Du, Baoxiang

doi:10.1016/j.aeue.2022.154242

Cited by 13 publications

(7 citation statements)

References 42 publications

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“…The double parameter Lyapunov exponent spectrum [33] can characterize the chaotic properties of a system. The double parameter Lyapunov exponent spectrum can observe the changes in the chaotic characteristics of a system under different parameters, with the horizontal and vertical axes representing two control parameters.…”

Section: The Double Parameter Lyapunov Exponentmentioning

confidence: 99%

Dynamical analysis and circuit realization of a high complexity fourth-order double-wing chaotic system with transient chaos and its application in image encryption

Zhang,

Bi,

Guo

et al. 2024

Phys. Scr.

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This paper proposes a fourth-order double-wing chaotic system with high complexity. After conducting a dynamic analysis, it is found that the system exhibits transient chaos and a rare inverse period-doubling bifurcation phenomenon in the bifurcation diagram. The system also exhibits attractor coexistence, with periodic, quasi-periodic, indicating high sensitivity to initial values. These phenomena sufficiently demonstrate the rich dynamical characteristics of chaotic systems. By introducing an impulse function with a cosine function in the foundation of the proposed system, it is found that controllable wing number and staircase burst oscillations occur. Furthermore, the number of wings and oscillation periods vary with changes in parameters, which has significant implications in engineering applications. The circuit design and construction are carried out using the Multisim simulation software, and the digital circuit is realized by using a Field-Programmable Gate Array (FPGA). It is found that the simulation results and the actual implementation results are highly consistent with the phase portrait of the system, thus demonstrating the feasibility of the circuit. Finally, by combining the proposed system with a DNA encryption algorithm, a novel image encryption algorithm with multiple layers of encryption is designed, greatly enhancing the security of encrypted images. The security of this encryption algorithm is analyzed in terms of information entropy, key space, correlation, and resistance to attacks. It is found that the proposed encryption algorithm exhibits high confidentiality and resistance to attacks. The proposed system has significant reference value in secure communication when applied to image encryption.

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Section: The Double Parameter Lyapunov Exponentmentioning

confidence: 99%

Dynamical analysis and circuit realization of a high complexity fourth-order double-wing chaotic system with transient chaos and its application in image encryption

Zhang,

Bi,

Guo

et al. 2024

Phys. Scr.

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“…We build a conservative hyperchaotic system in four dimensions using an approach from the literature [26], the mathematical model of which is given by equation (1):…”

Section: Design Of Conservative Hyperchaotic System 21 Modeling Of 4d...mentioning

confidence: 99%

Cross-channel image encryption algorithm on the basis of a conservative hyperchaotic system

Zhao,

Sun,

Sun

et al. 2024

Phys. Scr.

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In image encryption, the traditional encryption means of scrambling and diffusion are widely used, but they fail to completely eliminate the correlation between the channels of the ciphertext image and still exist security risks. The selecting channel and position scrambling and cross-channel S-shaped diffusion methods proposed in this study push the encryption to a new depth. Compared with ordinary methods, it is more thorough in disrupting pixel positions, increases the complexity of pixel relationships between different channels, and substantially improves the unpredictability of encryption. To support this approach, we design a four-dimensional conservative hyperchaotic system with a very large hyperchaotic interval, which combines the high randomness of the conservative system and the broad key-space property of the hyperchaotic system, effectively defending against the risk of phase-space reconstruction aroused by missing attractors and reducing the possibility of being cracked. We deeply analyze the dynamic properties of the system by means of phase diagrams, bifurcation diagrams and Lyapunov exponents. The cross-channel scrambling and diffusion encryption algorithm designed based on this system not only ensures the security of image information during transmission, but also greatly enhances the ability to resist various attacks. The proposal of this method undoubtedly brings a secure solution to the field of image encryption.

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“…According to the method in [33], we propose a new three-dimensional chaotic system. The mathematical expression of this system is shown in Equation ( 1)…”

Section: Proposed 3d Chaotic Systemmentioning

confidence: 99%

“…In this study, the encrypted images underwent differential attack testing. The computation formulas for differential attack resistance are respectively shown in Equations ( 31)- (33).…”

Section: Adjacent Pixel Correlationmentioning

confidence: 99%

Adaptive Fast Image Encryption Algorithm Based on Three-Dimensional Chaotic System

Wang,

Leng,

Zhang

et al. 2023

Entropy

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This paper introduces a novel three-dimensional chaotic system that exhibits diverse dynamic behaviors as parameters vary, including phase trajectory offset behaviors and expansion–contraction phenomena. This model encompasses a broad chaotic range and proves suitable for integration within image encryption. Building upon this chaotic system, the study devised a fast image encryption algorithm with an adaptive mechanism, capable of autonomously determining optimal encryption strategies to enhance algorithm security. In pursuit of heightened encryption speed, an FPGA-based chaotic sequence generator was developed for the image encryption algorithm, leveraging the proposed chaotic system. Furthermore, a more efficient scrambling algorithm was devised. Experimental results underscore the superior performance of this algorithm in terms of both encryption duration and security.

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Modeling methods and characteristic analysis of new Hamiltonian and non-Hamiltonian conservative chaotic systems

Cited by 13 publications

References 42 publications

Dynamical analysis and circuit realization of a high complexity fourth-order double-wing chaotic system with transient chaos and its application in image encryption

Dynamical analysis and circuit realization of a high complexity fourth-order double-wing chaotic system with transient chaos and its application in image encryption

Cross-channel image encryption algorithm on the basis of a conservative hyperchaotic system

Adaptive Fast Image Encryption Algorithm Based on Three-Dimensional Chaotic System

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