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.

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This work introduce a new high dimensional 10-D hyperchaotic system with high complexity and many of coexisting attractors. With the adjustment of its parameters and initial points, the novel system can generate periodic, quasi-periodic, chaotic, and hyperchaotic behaviours. For special values of parameters, we show that the proposed 10-D system has a very high Kaplan-Yorke fractal dimension, which can reach up to 9.067 indicating the very complexity of the 10-D system dynamics. In addition, the proposed system is shown to exhibit at least six varied attractors for the same values of parameters due to its multistability. Regions of multistability are identified by analysing the bifurcation diagrams of the proposed model versus its parameters and for six different values of initial points. Many of numerical plots are given to show the appearance of different dynamical behaviours and the existence of multiple coexisting attractors. The main problem with controlling chaos/hyperchaos systems is that they are not always fully synchronized. therefore, some powerful synchronization techniques should be considered. The synchronization between the high-dimensional 10-D system and a set of three low-dimensional chaotic and hyperchaotic systems is proposed. Ten control functions are designed using the active control method, ensuring synchronisation between the collection of systems and the 10-D hyperchaotic system. Finally, using Multisim 13.0 software to construct the new system’s electronic circuit, the feasibility of the new system with its extremely complicated dynamics is verified. Therefore, the novel 10-D hyperchaotic system can be applied to different chaotic-based application due to its large dimension, complex dynamics, and simple circuit architecture.

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