A multi-wing spherical chaotic system using fractal process

Abstract

In this paper, a multi-wing spherical chaotic system is derived via a fractal process based on Qi 3D four-wing chaotic system. The system can generate a 4n-wing chaotic system. Numerical simulations demonstrate the validity and feasibility of the proposed method, which may generate multi-wing chaotic systems not only using the Qi 3D four-wing system but also other 3D autonomous chaotic systems. Compared with other multi-wing chaotic attractors, the proposed multi-wing chaotic attractors are much easier to adjust the number of the wings. Hamiltonian energy formulas of both original system and the transformed system are obtained, which concludes that the energy is decreased as the multi-wing number increased. Poincare map and bifurcation analysis show that the newly generated system has extremely rich dynamics and the topological structure is much more complicated than the original system. The 4n-wing chaotic system is more suitable for the further research on the application of chaos encryption than the original chaotic system.