Design and practical implementation of a novel hyperchaotic system generator based on Apéry's constant

Abstract

Modern chaotic systems necessitate high levels of randomness and complexity, which can be achieved through adaptable seed functions. This paper proposes a new 2D Apéry chaotic system generator (2D-ACG) based on Apéry numbers to fulfill this need. The 2D-ACG generates various chaotic systems using classical seed functions. The effectiveness and the capabilities of 2D-ACG are demonstrated on three well-known example chaotic maps using pairs of seed functions such as Cos-Cos, Sin-Sin and Cos-Sin. The reliability of chaos metrics, such as the Lyapunov exponent (LE), sample entropy (SE), correlation dimension (CD), Kolmogorov entropy (KE), C0 test, and sensitivity, confirms the chaotic performance of these maps. This is further supported by a comparison with reported 2D chaotic systems. Furthermore, one of the maps derived from 2D-ACG has been implemented into an image encryption algorithm and has successfully passed the cryptanalysis tests. Additionally, the hardware implementation of 2D-ACG has been tested on a field programmable gate array (FPGA), thereby confirming its efficacy. The superior results obtained indicate that the proposed 2D-ACG, with its enhanced diversity and complex structure derived from the Apéry's constant, exhibits higher-performance chaotic characteristics.