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

Zhou, Xuejiao; Li, Chunbiao; Lu, Xu; Lei, Tengfei; Zhao, Yi

doi:10.3390/sym13061047

Cited by 8 publications

(2 citation statements)

References 35 publications

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“…Some dynamical systems, whether defined in continuous or discrete time, have been implemented through electronic circuits and have been given different uses. For example, the implementation of such chaotic systems has been used in image encryption schemes, secure communication systems, etc., and has been done through the use of different electronic devices such as field programmable analog arrays (FPAAs) [4], the platform STM32 [5], and FPGAs [6]. These different devices have some advantages and disadvantages, for example, in an FPAA device the processing time is less compared to digital devices because it does not require discretization and the blocks are already established.…”

Section: Introductionmentioning

confidence: 99%

FPGA Implementation of a Chaotic Map with No Fixed Point

et al. 2023

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The employment of chaotic maps in a variety of applications such as cryptosecurity, image encryption schemes, communication schemes, and secure communication has been made possible thanks to their properties of high levels of complexity, ergodicity, and high sensitivity to the initial conditions, mainly. Of considerable interest is the implementation of these dynamical systems in electronic devices such as field programmable gate arrays (FPGAs) with the intention of experimentally reproducing their dynamics, leading to exploiting their chaotic properties in real phenomena. In this work, the implementation of a one-dimensional chaotic map that has no fixed points is performed on an FPGA device with the objective of being able to reproduce its chaotic behavior as well as possible. The chaotic behavior of the introduced system is determined by estimating the Lyapunov exponents and its chaotic behavior is also analyzed using bifurcation diagrams. Simulations of the system are realized via Matlab, as well as in C and the very high-speed integrated circuit (VHSIC) hardware description language (VHDL). Experimental results on FPGA show that they are like those obtained in the simulations; therefore, this chaotic dynamical system could be used as an element in some encryption schemes such as in the generation of cryptographically secure pseudorandom numbers.

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Section: Introductionmentioning

confidence: 99%

FPGA Implementation of a Chaotic Map with No Fixed Point

et al. 2023

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“…For real-world applications, we have designed an electronic circuit of the new hyperchaotic four-wing system using MultiSim. Circuit design of hyperchaotic systems is useful in practical applications [29,30].…”

Section: Introductionmentioning

confidence: 99%

A new 4-D hyperchaotic four-wing system, its bifurcation analysis, complete synchronization and circuit simulation

2023

Archives of Control Sciences

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In this work, we modify the dynamics of 3-D four-wing Li chaotic system (Li et al. 2015) by introducing a feedback controller and obtain a new 4-D hyperchaotic four-wing system with complex properties. We show that the new hyperchaotic four-wing system have three saddle-foci balance points, which are unstable. We carry out a detailed bifurcation analysis for the new hyperchaotic four-wing system and show that the hyperchaotic four-wing system has multistability and coexisting attractors. Using integral sliding mode control, we derive new results for the master-slave synchronization of hyperchaotic four-wing systems. Finally, we design an electronic circuit using MultiSim for real implementation of the new hyperchaotic four-wing system.

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A memristive chaotic map with only one bifurcation parameter

Li,

Zhong

et al. 2024

Nonlinear Dyn

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

Cited by 8 publications

References 35 publications

FPGA Implementation of a Chaotic Map with No Fixed Point

FPGA Implementation of a Chaotic Map with No Fixed Point

A new 4-D hyperchaotic four-wing system, its bifurcation analysis, complete synchronization and circuit simulation

A memristive chaotic map with only one bifurcation parameter

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