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A New 4-D Hyperchaotic System with No Balance Point, Its Bifurcation Analysis, Multi-Stability, Circuit Simulation, and FPGA Realization

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Complex Systems and Their Applications

Abstract

This work proposes a new 4-D hyperchaotic system with three quadratic nonlinear terms. We establish that the proposed system has no balance point. We deduce that the system has hidden attractors. We carry out a dynamic analysis of the new system with bifurcation diagrams and Lyapunov exponents. We show that the new system has multi-stability and coexisting attractors. Using MultiSim Version 14, we design an electronic circuit of the new hyperchaotic system. The new 4-D hyperchaotic system with no balance point is verified under an implementation using a field-programmable gate array (FPGA). We show the block diagrams’ descriptions of the system by applying three one-step numerical methods, which consist of multipliers, adders, and subtractors, and we list the hardware resources required for each numerical method. Finally, we show the experimental hyperchaotic attractors, which are in good agreement with simulation results.

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Correspondence to Sundarapandian Vaidyanathan .

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Vaidyanathan, S., Tlelo-Cuautle, E., Guillén-Fernández, O., Benkouider, K., Sambas, A. (2022). A New 4-D Hyperchaotic System with No Balance Point, Its Bifurcation Analysis, Multi-Stability, Circuit Simulation, and FPGA Realization. In: Huerta Cuéllar, G., Campos Cantón, E., Tlelo-Cuautle, E. (eds) Complex Systems and Their Applications. Springer, Cham. https://doi.org/10.1007/978-3-031-02472-6_9

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