Generation of n-dimensional complex chaotic system via parameter matrix configuration

Abstract

Complex chaotic systems can exhibit high chaotic complexity due to the presence of complex variables and complex parameters. Most research has focused on real chaotic systems, but complex chaotic systems remain relatively under-explored. To this end, this work presents an $n$-dimensional complex chaotic system ($n$D-CCS) generation method utilizing complex parametric Pascal matrices. Initially, these matrices are generated and subsequently utilized as the parameter matrices for constructing the $n$D chaotic systems. Theoretical analysis demonstrates that the proposed $n$D-CCS can exhibit chaotic behavior. Extensive experiments show that the $n$D-CCS possesses more robust chaotic performance than existing $n$D real chaotic systems. To demonstrate the effectiveness of our method, a four-dimensional complex chaotic map (4D-CCM) is generated and its chaotic behavior is analyzed. Furthermore, we develop a hardware platform to verify the 4D-CCM’s implementation on hardware devices. We also design pseudorandom number generators (PRNGs) using the 4D-CCM and test their randomness against the NIST SP800-22 standard. The result indicates excellent randomness in the PRNGs.