Generation of 2N + 1-scroll existence in new three-dimensional chaos systems

We propose a systematic methodology for creating 2N + 1-scroll chaotic attractors from a simple three-dimensional system, which is named as the translation chaotic system. It satisfies the condition a₁₂a₂₁ = 0, while the Chua system satisfies a₁₂a₂₁ > 0. In this paper, we also propose a successful (an effective) design and an analytical approach for constructing 2N + 1-scrolls, the translation transformation principle. Also, the dynamics properties of the system are studied in detail. MATLAB simulation results show very sophisticated dynamical behaviors and unique chaotic behaviors of the system. It provides a new approach for 2N + 1-scroll attractors. Finally, to explore the potential use in technological applications, a novel block circuit diagram is also designed for the hardware implementation of 1-, 3-, 5-, and 7-scroll attractors via switching the switches. Translation chaotic system has the merit of convenience and high sensitivity to initial values, emerging potentials in future engineering chaos design.