Two-Dimensional Coupled Complex Chaotic Map

Chaotic systems have attracted extensive research due to their pseudorandomness, ergodicity, and unique properties. Most studies focus on chaotic systems in the real number domain, but recent research has explored the design of complex chaotic systems. However, the chaotic behaviors of previous complex chaotic systems can only be observed through experiments and lack theoretical proof. In this article, we construct a 2-D coupled complex chaotic (2D-CCC) map using two nonlinear functions in the complex number domain. We theoretically prove the robust and complex chaotic behavior of the 2D-CCC map using the Lyapunov exponent. In addition, we conduct extensive experiments to demonstrate the map's intricate dynamics and high performance indicators. Comparison results highlight its superiority over previous chaotic systems. We also implement our 2D-CCC map on a hardware platform to validate its implementation feasibility on hardware devices. Finally, we investigate the 2D-CCC map's application in pseudorandom number generation and the testing results validate the high degree of randomness in the generated pseudorandom numbers.