SLSS-3D: a robust 3D hyperchaotic map with coupled transformations

Chaotic systems, known for their unique dynamics, are used in cryptography, neural networks, control engineering, and secure communications. However, some classical and improved hyperchaotic systems may have security issues due to insufficient complexity. To address this problem, this study proposes a novel 3D <strong>hyperchaotic map</strong> named <strong>SLSS-3D</strong>. The SLSS-3D system derives from classical logistic, sine, and ICMIC maps through nonlinear coupling transformations. It includes two control parameters, α and β, offering a wider range of parameter selection. This enhances resistance to bruteforce attacks. This study evaluates the <strong>hyperchaotic behavior</strong> of the SLSS-3D system through analyses of phase diagrams, bifurcation diagrams, Lyapunov exponent spectra, sample entropy, the 0-1 test, and permutation entropy. The findings reveal that the SLSS-3D system demonstrates superior stability and significant chaotic properties. These characteristics suggest that SLSS-3D has substantial potential for applications in cryptography, artificial intelligence, and secure communications.