Generation of one-dimensional complex discrete hyperchaotic maps with hardware implementation

Due to the presence of complex variables and parameters, complex chaotic systems exhibit rich dynamical behaviors and high chaos complexity for diverse chaos-based applications. However, most existing studies have focused on real chaotic systems, while their complex counterparts remain relatively under-explored. In light of this, we propose a novel one-dimensional complex chaotic system (1D-CCS) that can generate various 1D complex chaotic maps by integrating the remainder operation with various analytic functions. To demonstrate its effectiveness, two representative maps are constructed. Theoretical analysis shows that one example satisfies the chaos definition in terms of Lyapunov exponent, with the exponent explicitly determined by system parameters. Property studies reveal that the generated maps exhibit abundant chaotic behaviors. Extensive experiments further manifest that the proposed chaotic maps possess higher chaos complexity compared to representative existing maps. To investigate their digital characteristics, state-mapping networks are constructed using various fixed-point precision settings, and several numerical measures are employed to evaluate digital periodicity and convergence. A microcontroller-based platform is then constructed to implement the two complex chaotic maps, from which two-channel complex chaotic sequences and attractor diagrams are experimentally obtained. Finally, the pseudorandom number generators are developed to demonstrate the potential applicability of the generated maps.