A New 5-D Multistable Hyperchaotic System With Three Positive Lyapunov Exponents: Bifurcation Analysis, Circuit Design, FPGA Realization and Image Encryption

Abstract

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.

Hybrid Analog Computer for Modeling Nonlinear Dynamical Systems: The Complete Cookbook

“…Even this very special feature does not prevent the design engineer from successive realization. Of course, interesting FPGA-based realizations can be found in other publications, such as [ 41 , 42 , 43 , 44 , 45 ].…”

A new 4‐D hyperchaotic two‐scroll system with hidden attractor and its field‐programmable gate array implementation

“…The hardware design of a chaotic system can be performed using the MATLAB tool known as Simulink, 17 but the designer cannot take control on the manipulation of bits, as done when using numerical methods to discretize the block description of a dynamical system. 16 The use of the chaotic systems implemented on FPGAs is quite important in applications as for the development of digital chaotic communication systems, as shown in Capligins et al, 17 where the authors claim the FPGA design of a modified Chua's circuit along an antipodal chaotic shift keying modulation provide high security on the physical communication level and can be used in wireless sensor network systems. On this regard, as a hyperchaotic system provides better chaotic behavior than Chua's circuit, several applications can be enhanced using our proposed FPGA design of the new 4-D hyperchaotic two-scroll system with hidden attractor.…”

“…As shown in Benkouider et al, 16 the application of numerical methods is quite useful to discretize the continuous time equations describing a dynamical system. The most simple and commonly used numerical method is the forward Euler (FE), so that by applying this method to the hyperchaotic system given in (1), the discretized equations are given in (6).…”

“…Recent works show the implementation of hyperchaotic systems using field‐programmable gate arrays (FPGA), as they have advantages for fast verification and prototyping, as already shown in previous works 16,17 . The hardware design in this case makes use of fixed‐point notation to perform computer arithmetic, and the length of the number of bits that are used to process the signals depends on the amplitudes of the state variables of the dynamical system.…”

“…Recent works show the implementation of hyperchaotic systems using field-programmable gate arrays (FPGA), as they have advantages for fast verification and prototyping, as already shown in previous works. 16,17 The hardware design in this case makes use of fixed-point notation to perform computer arithmetic, and the length of the number of bits that are used to process the signals depends on the amplitudes of the state variables of the dynamical system. In some cases, the amplitudes can be downscaled to be within desirable values, so that one can design the systems using integrated circuit (IC) technology, which allow amplitudes around ±1, as recently shown in Valencia-Ponce et al 18 In this work, the new 4-D hyperchaotic two-scroll system with hidden attractor is prototyped using the FPGA Zybo Z7-20 development board, and a scaling process is performed to observe the experimental attractors, as detailed in Section 6.…”