Power-\(\alpha \) chaotic system with robust chaos

Robust chaos is characterized by the absence of periodic windows and coexisting attractors across a chaotic system’s parameter space. It is important for applications demanding stable chaos. This paper proposes the Power- \(\alpha \) $\alpha$ Map (P- \(\alpha \) $\alpha$ M) system which includes the 1-D and N-D P- \(\alpha \) $\alpha$ M systems. The 1-D P- \(\alpha \) $\alpha$ M system is designed to generate one-dimensional robust chaotic maps, and we further demonstrate that some classic chaotic maps can be represented by the linear combinations of some 1-D P- \(\alpha \) $\alpha$ M functions. Based on the 1-D P- \(\alpha \) $\alpha$ M, we further develop a method to generate arbitrary N-D P- \(\alpha \) $\alpha$ M hyperchaotic system. Multi-perspective performance analyses demonstrate that the proposed 1-D and N-D P- \(\alpha \) $\alpha$ M systems are robust chaotic in a large parameter space.