A Symmetric Controllable Hyperchaotic Hidden Attractor

Zhang, Xin; Li, Chunbiao; Lei, Tengfei; Liu, Zuohua; Tao, Changyuan

doi:10.3390/sym12040550

Cited by 18 publications

(9 citation statements)

References 41 publications

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“…Despite significant progress in the study of chaotic systems, challenges remain, particularly in the generation and transmission of broadband chaotic signals with appropriate amplitude and polarity [14]. Amplitude control and offset boosting have emerged as promising techniques to manipulate the dynamical behavior of chaotic systems for practical applications.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis and circuit realization of a new controllable hyperchaotic system

Lalili,

Bouden,

Grimes

et al. 2024

Phys. Scr.

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Amidst the realm of hyper-chaotic systems, a notable deficiency is the absence of amplitude control and signal polarity. This paper addresses this limitation by introducing a new 4-D hyper-chaotic system with a hidden equilibrium-free attractor. The study focuses on amplitude control, achieved by adjusting a specific parameter, enabling manipulation of variable magnitudes while maintaining the overall signal. The offset boosting technique is investigated, enabling flexible shifting of the attractor in a desired direction. A real circuit experiment validates the proposed system's practical applicability, confirming consistency with theoretical analysis and numerical simulations. Through introducing this new-found, the study holds significant importance for various fields, such as communications engineering and chaos-based cryptography, where precise control of signal characteristics is paramount.

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Section: Introductionmentioning

confidence: 99%

Dynamic analysis and circuit realization of a new controllable hyperchaotic system

Lalili,

Bouden,

Grimes

et al. 2024

Phys. Scr.

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show abstract

“…In recent years, many scholars have proposed new chaotic systems. However, due to the small key space and simple chaotic orbits of one-dimensional chaotic mapping, highdimensional chaotic systems are increasingly researched by scholars [12][13][14][15]. In 2009, Bao et al added a linear term to their presented new chaotic system equation to obtain a simple four-dimensional hyperchaotic system [12].…”

Section: Introductionmentioning

confidence: 99%

“…In 2015, Chen Y M et al designed a new four-dimensional hyperchaotic system with equilibrium curves by improving the Lorenz system and discovered the existence of four different types of coexisting attractors [13]. In 2020, Zhang X et al discovered a hyperchaotic system without an equilibrium point by adding feedback to the equations of a Lorenz-like system, which allows the system to be amplitude controlled and offset by an independent knob [14]. In 2021, Yang et al constructed a four-dimensional memristor hyperchaotic system based on the Liu chaos system by introducing a flux-controlled memristor model [15].…”

Section: Introductionmentioning

confidence: 99%

Design of a new four-dimensional chaotic system and its application to color image encryption

Yan

Zhao³

2023

Preprint

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In this paper, a new four-dimensional chaotic system is constructed. Then, the dynamics of the phase diagram, Lyapunov exponent, bifurcation, and complexity of the system are investigated, the simulation circuit of the system is designed and the trajectory simulation of the system is implemented using a Field Programmable Gate Array (FPGA). National Institute of Standards and Technology (NIST) tests have verified the randomness of the output of the chaotic sequence by the system. Finally, a new color image encryption algorithm is designed based on this system. In the proposed algorithm, the plaintext information is used to generate the initial value of the system through a hashing algorithm, and the plaintext information is applied to the algorithm, reflecting the idea of algorithmic adaption. The bit-plane decomposition row dislocation breaks the strong correlation between pixels, and finally, the DNA encoding is combined with the diffusion method to complete the complete encryption process. Multiple security analysis methods show that the scheme has a good encryption effect.

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“…However, there is still much work to do for the rescaling of broadband chaotic sequences. Difficulty modulation with broadband chaotic signal, amplitude [10][11][12][13], symmetry [14][15][16][17], and multistability [18][19][20][21] have been extensively studied in a nonlinear field. In practical engineering applications, linear transformations are usually necessary but sometimes are unpermitted to obtain the required geometric scale in designed hardware.…”

Section: Introductionmentioning

confidence: 99%

A 2D Hyperchaotic Map: Amplitude Control, Coexisting Symmetrical Attractors and Circuit Implementation

Zhou

et al. 2021

Symmetry

Self Cite

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An absolute value function was introduced for chaos construction, where hyperchaotic oscillation was found with amplitude rescaling. The nonlinear absolute term brings the convenience for amplitude control. Two regimes of amplitude control including total and partial amplitude control are discussed, where the attractor can be rescaled separately by two independent coefficients. Symmetrical pairs of coexisting attractors are captured by corresponding initial conditions. Circuit implementation by the platform STM32 is consistent with the numerical exploration and the theoretical observation. This finding is helpful for promoting discrete map application, where amplitude control is realized in an easy way and coexisting symmetrical sequences with opposite polarity are obtained.

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A Symmetric Controllable Hyperchaotic Hidden Attractor

Cited by 18 publications

References 41 publications

Dynamic analysis and circuit realization of a new controllable hyperchaotic system

Dynamic analysis and circuit realization of a new controllable hyperchaotic system

Design of a new four-dimensional chaotic system and its application to color image encryption

A 2D Hyperchaotic Map: Amplitude Control, Coexisting Symmetrical Attractors and Circuit Implementation

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