Estimation and modeling of novel hyperchaotic and fractional order Jerk systems for image encryption

Abstract

This paper presents a systematic comparative analysis of seven hyperchaotic and fractional order Jerk systems for secure communication applications. Key dynamical metrics — Lyapunov exponents, Kaplan–Yorke dimensions, and attractor characteristics — are computed under identical simulation conditions using the Benettin–Wolf algorithm. The results reveal that four-dimensional and fractional order architectures consistently outperform classical third-order models, while hidden attractors provide additional structural security. Three systems satisfy the high-performance criteria ($L{E}_1>0.15$, $D_{KY}>2.8$); notably, the fractional order hypogenetic memristive system achieves the highest sensitivity ($L{E}_1=0.7374$, $D_{KY}=3.281$), whereas the integer-order hidden hyperchaotic system offers an optimal trade-off between dynamical complexity, structural security, and implementation efficiency. To validate practical applicability, the latter system is implemented in a complete image encryption scheme. Experiments on standard test images achieve near-ideal entropy (up to 7.9999), strong differential resistance (NPCR $>99.6\text{\%}$, UACI $\in [32.44\text{\%},33.51\text{\%}]$), and near-zero correlation coefficients, outperforming several recent state-of-the-art methods.