Automatic Design of Multi-Fold Hyperchaotic System Using Parallel Fractal Algorithm

This brief presents a simple one-step parallel fractal algorithm for automatic design of multi-fold hyperchaotic system from scroll/wing-type seed system. It is shown that the desired number of folds can be generated via a simple parametric control. Two representative application cases of four-dimensional and six-dimensional multi-fold no-equilibrium hyperchaotic systems are presented. For a double-wing seed attractor, the method will generate $2^{m}$ wings under each pair of m-fold transformation. In contrast with existing designs, the proposed algorithm is automatic and has wide applicability in generating various numbers of folds in multiple directions. Simulation studies and hardware implementations are conducted to verify the feasibility of the proposed algorithm.