Novel two-directional grid multi-scroll chaotic attractors based on the Jerk system

Ding, Pengfei; Wu, Chengmao

doi:10.1088/1674-1056/ab9dea

Cited by 15 publications

(15 citation statements)

References 79 publications

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“…Thus, based on the quadratic transformation, system (1) is transformed into system (6). Next, the characteristics of the equilibrium points and their eigenvalues are analyzed.…”

Section: A Four-wing Chaotic System Based On the Quadratic Transforma...mentioning

confidence: 99%

“…The distribution of those equilibrium points in x-y plane is shown in Fig. 1, in which the symbol '⋆' represents the equilibrium points of system (6).…”

Section: A Four-wing Chaotic System Based On the Quadratic Transforma...mentioning

confidence: 99%

“…[39] 3. A switched chaotic system based on a class of switching functions Clearly, for system (6), there exists a one-to-one correspondence between the number of saddle-focus points and the number of wings. In this section, by constructing a class of switching functions, the number of saddle-focus equilibrium points with index 2 on both sides of the origin can be increased.…”

Section: Equilibrium Pointsmentioning

confidence: 99%

“…The distribution of those equilibrium points 020507-5 in x-y plane is exhibited in Fig. 9, in which the symbol ' ' represents the equilibrium points obtained in case 4 and '⋆' denotes the equilibrium points of the original system (6). Obviously, the equilibrium points have been expanded from the previous four to sixteen.…”

Section: Equilibrium Pointsmentioning

confidence: 99%

“…At present, design and implementation of multi-wing or multi-scroll chaotic systems with rich dynamic properties on the basis of chaos and circuit theory have become an important research topic. [1][2][3][4][5][6][7][8][9][10] The research on the generation of multi-scroll chaotic systems has been relatively mature, but it is still challenging to design the multi-wing chaotic systems. Compared with conventional 2-wing chaotic systems, multiwing chaotic systems not only have more key parameters, but also have nested topological structures.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Design and FPGA implementation of multi-wing chaotic switched systems based on a quadratic transformation*

Shi¹,

Huang²,

Yuan³

et al. 2021

Chinese Phys. B

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Based on a quadratic transformation and a switching function, a novel multi-wing chaotic switched system is proposed. First, a 4-wing chaotic system is constructed from a 2-wing chaotic system on the basis of a quadratic transformation. Then, a switching function is designed and by adjusting the switching function, the number and the distribution of the saddle-focus equilibrium points of the switched system can be regulated. Thus, a set of chaotic switched systems, which can produce 6-to-8-12-16-wing attractors, are generated. The Lyapunov exponent spectra, bifurcation diagrams, and Poincaré maps are given to verify the existence of the chaotic attractors. Besides, the digital circuit of the multi-wing chaotic switched system is designed by using the Verilog HDL fixed-point algorithm and the state machine control. Finally, the multi-wing chaotic attractors are demonstrated via FPGA platform. The experimental results show that the number of the wings of the chaotic attractors can be expanded more effectively with the combination of the quadratic transformation and the switching function methods.

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“…Thus, based on the quadratic transformation, system (1) is transformed into system (6). Next, the characteristics of the equilibrium points and their eigenvalues are analyzed.…”

Section: A Four-wing Chaotic System Based On the Quadratic Transforma...mentioning

confidence: 99%

“…The distribution of those equilibrium points in x-y plane is shown in Fig. 1, in which the symbol '⋆' represents the equilibrium points of system (6).…”

Section: A Four-wing Chaotic System Based On the Quadratic Transforma...mentioning

confidence: 99%

Section: Equilibrium Pointsmentioning

confidence: 99%

Section: Equilibrium Pointsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Design and FPGA implementation of multi-wing chaotic switched systems based on a quadratic transformation*

Shi¹,

Huang²,

Yuan³

et al. 2021

Chinese Phys. B

View full text Add to dashboard Cite

show abstract

Generation multi-scroll chaotic attractors using composite sine function and its application in image encryption

Ding,

Li,

Wang

2024

Phys. Scr.

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In this paper, a composite sine function is proposed and applied in a chaotic system, which is capable of generating definite number of chaotic attractors. The proposed composite sine function possesses infinite breakpoints, but it can produce a fixed number of scrolls by adjusting its parameters. Compared to other chaotic systems with multiple scrolls chaotic attractors, the realization circuit of the chaotic system with compound sine function allows obtaining different numbers of scrolls by adjusting only one resistance value. As a result, the circuit structure remains unchanged despite variations in the number of scrolls. Various analytical methods are applied to study the dynamical behaviors of the proposed chaotic system, including Lyapunov exponent, equilibrium point, bifurcation diagram,algorithm. Furthermore, phase diagram, spectral entropy and C0-based on the analysis of dynamical characteristics, theelectronic circuits of the proposed system are given on Multisim circuit simulationsoftware, and the multi-scroll chaotic attractors exhibit consistency with the numericalsimulation results. Finally, we incorporated the proposed chaotic system into a DNA coding algorithm for image encryption, and this method exhibits excellent encryption efficiency and high level of security.

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Design and analysis of image encryption based on memristor chaotic systems with hidden attractors

Ding,

Wang,

2024

Phys. Scr.

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Chaotic systems with hidden attractors are important research hotspots in nonlinear science. In recent years, continuous chaotic systems with special equilibrium points have been widely studied, especially continuous chaotic systems without equilibrium points. A four-dimensional chaotic system devoid of equilibrium point is proposed by using a composite cosine piecewise-linear (COS-PWL)function and a memristor model based on the modified Sprott-C system. The dynamical behaviors of the new system are studied through numerical analysis methods. The results reveal it is extremely sensitive to control parameters as well as initial conditions, which make it particularly suitable for application to image encryption algorithms. In light of these findings, a novel image encryption algorithm is introduced. This algorithm integrates the new four-dimensional chaotic system with ribonucleic acid (RNA) coding technology. Furthermore, the simulation results and security analyses validate the rationality of the encryption mechanism and the robustness of the encryption security of the proposed image encryption algorithm.

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Novel two-directional grid multi-scroll chaotic attractors based on the Jerk system

Cited by 15 publications

References 79 publications

Design and FPGA implementation of multi-wing chaotic switched systems based on a quadratic transformation*

Design and FPGA implementation of multi-wing chaotic switched systems based on a quadratic transformation*

Generation multi-scroll chaotic attractors using composite sine function and its application in image encryption

Design and analysis of image encryption based on memristor chaotic systems with hidden attractors

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