Complex-valued chaotic model with high chaos complexity and provable Lyapunov exponent

Abstract

Chaotic systems with high chaos complexity are the foundation of chaos-based applications. Owing to the existence of complex-valued variables and parameters, complex chaotic systems can exhibit intricate dynamics and high chaos complexity. Yet, research in this area remains largely concentrated on real chaotic systems. In light of this, we propose a two-dimensional complex chaotic model (2D-CCM) by combining modular operation and various entire functions. This framework enables the systematic generation of diverse two-dimensional complex chaotic maps suitable for chaos-based applications. To show its capability, two illustrative examples are presented and analyzed. Unlike most studies that rely solely on numerical validation, we provide a theoretical guarantee for the chaotic behavior exhibited by the proposed maps. Property analysis further reveals that the two complex maps exhibit rich dynamical behaviors with diverse chaotic features. Extensive experiments show that the generated maps outperform several representative systems in terms of chaos complexity metrics and have also been successfully implemented in hardware platform. In addition, pseudorandom number generators are constructed using the generated maps. The resulting sequences exhibit strong statistical randomness, as verified by both the NIST SP 800-22 and TestU01 test suites. Finally, when applied to the FH-OFDM-DCSK system under AWGN channels, they achieve lower bit error rates than existing maps. This highlights their robustness to noise and potential for secure applications.