nD-CS: A circularly shifting chaotic map generation method

Due to more complex behavior and larger number of control parameters, high-dimensional chaotic map generation methods may provide more satisfactory performance in various practical applications compared to low-dimensional counterparts. Designing n-dimensional (nD) chaotic map generation methods for generating chaotic maps in arbitrary dimensions with desired dynamics is an interesting but challenging task. In this paper, we propose a universal framework called the nD circularly shifting chaotic map generation method (nD-CS), which utilizes existing one-dimensional chaotic maps as seed maps to generate nD chaotic maps with complex and robust behaviors. Theoretical analysis proves that when specific criteria are met by its control parameters, our nD-CS can exhibit complex and robust hyperchaotic behavior in the sense of Lyapunov exponent. To demonstrate the effectiveness of our nD-CS, we first employ it to generate three examples of three-dimensional hyperchaotic maps. The results indicate high-performance indicators of these new chaotic maps. Furthermore, we compare the nD chaotic maps generated by our nD-CS to those produced by existing methods. The results demonstrate that our chaotic maps have a better overall performance.