Rem-based complex-valued hyperchaotic system with provable chaotic dynamics

Owing to the presence of complex variables and parameters, complex-valued chaotic maps can show abundant dynamical behaviors and high chaos complexity, and thus have been widely utilized in various chaos-based applications. However, the majority of existing studies concentrate on real-valued chaotic maps. In light of this, this article proposes a two-dimensional complex-valued hyperchaotic system (2D-CHS) that can generate diverse 2D complex-valued hyperchaotic maps. The 2D-CHS is constructed by combining existing 2D real-valued chaotic seed maps with the remainder operation to generate complex-valued hyperchaotic maps, which are designed for flexible construction and enhanced chaos complexity. Compared with existing complex-valued chaotic maps, the proposed system is more flexible and achieves higher chaos complexity. To validate the effectiveness of the 2D-CHS, two representative maps are provided. Theoretical proof displays that the proposed map possesses chaotic property in the perspective of Lyapunov exponent. Dynamical analysis reveals that both maps exhibit abundant dynamical behaviors in the complex domain. Extensive experiments demonstrate that the proposed maps achieve high chaos complexity, including a correlation dimension of 1.9907, a permutation entropy of 0.9996, a Kolmogorov entropy of 1.5044, and a sample entropy of 1.8106. In addition, a hardware platform is constructed to show strong agreement with those obtained from software simulations. Finally, pseudorandom number generators are developed, and the produced random numbers achieve a 100% pass rate in the TestU01 test suite.