Algorithmic design of n-dimensional multifold system via cyclic fractal process

The generation of folded trajectories for simple chaotic and hyperchaotic systems can produce complicated multiscroll or multiwing attractors, which have shown specific industrial applications. Although various methods have been reported, rare of them have wide applicability in different types of higher-dimensional systems. To address this issue, this paper presents a universal computer-aided algorithmic design for automatic generation of chaotic and hyperchaotic multifold system from simple seed system with a dimension greater than or equals to three. Specifically, a universal cyclic fractal algorithm based on Julia transformation is presented. By selecting chaotic and hyperchaotic systems as the seeds, the application of the algorithm has automatically yielded corresponding multifold systems with complicated folding trajectories. In comparison with existing methods, significant novelty of the algorithmic design is that neither extra dimension nor excitation was introduced to the seed system. We have presented various numerical demonstrations to show the generation of different numbers of fold from different systems. Finally, the hardware experiment is presented for verification and laying the groundwork for potential engineering applications.