In this work, we describe the model of a new 5-D hyperchaotic system with three positive Lyapunov exponents. Since the maximum positive Lyapunov exponent of the proposed hyperchaotic system is larger than twelve, the new hyperchaotic system is highly hyperchaotic. We also show that the new 5-D hyperchaotic system exhibits multistability with coexisting attractors. Using Multisim, we design an electronic circuit for the new 5-D hyperchaotic system. The hardware implementation of the new 5-D hyperchaotic system is done by applying two numerical methods. From the experimental results of the FPGA-based implementation, we show that the attractors observed in a Lecroy oscilloscope are in good agreement with numerical simulations. To prove the reliability of the proposed system for cybersecurity purposes, we presented a new image cryptosystem using our hyperchaotic system. Experimental outcomes show the efficiency and the reliability of our cryptosystem based on the proposed hyperchaotic system.INDEX TERMS Hyperchaos, bifurcations, multi-stability, attractors, Lyapunov exponents, circuit design, FPGA, numerical methods, data security; image cryptosystem.
A challenge in the physical design of η-scroll attractors is to generate a large number of scrolls.However, an open question is: Does the large number of scrolls determine a better chaotic behavior? We present a partial answer to this question by computing the Lyapunov exponents for piecewise-linear (PWL) functions based on η-scroll third order chaotic oscillators, namely: Zhong modified Chua's circuit, Yu modified Chua's circuit, saturated function series based chaotic oscillator, and generalized Chua's circuit with saw-tooth function. Three different integration methods (forward Euler, fourth order Runge Kutta and Matlab c ODE 45) are used in order to show that the positive Lyapunov exponent is not significantly incremented in relation with the number of scrolls.
This paper introduces the guidelines to synthesize 2D chaotic systems by means of high‐level descriptions. The aim of this investigation is to synthesize 2D‐n‐scrolls chaotic systems based on saturated functions with multisegments. The new methodology of circuit synthesis is performed by three hierarchical levels. First, the 2D chaotic oscillator is numerically simulated at the electronic system level by applying state variables and piecewise‐linear approximation. Second, the excursion levels of the chaotic signals are scaled to control the breaking points and slopes of the saturated functions within practical values. Additionally, the frequency scaling of 2D‐n‐scrolls chaotic attractors is performed. Finally, current and voltage saturated functions are synthesized using Verilog‐A models for the operational amplifiers and in this manner a 2D chaotic system is synthesized using operational amplifiers to generate 2D‐n‐scrolls attractors. Numerical results are confirmed by H‐SPICE simulations to show the usefulness of the proposed synthesis approach.
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