This research conducts a comprehensive analysis of the commensurate fractional-order gyrostat system, resolving significant gaps in current literature. The chaotic dynamics are analyzed through Lyapunov exponent calculations, and the attractor’s fractal properties are characterized via the Kaplan-Yorke dimension. Bifurcation diagrams elucidate transitions between periodic and chaotic states, while system stability is established based on the stability theory of commensurate fractional-order systems. The system complexity is evaluated using spectral entropy (SE) and \(C_{0}\) complexity metrics. Generated sequences undergo rigorous NIST SP 800-22 statistical test, verifying their randomness and cryptographic viability for secure implementations. Leveraging the fractional gyrostat system’s inherent entropy richness and parametric sensitivity, an efficient scheme for encrypting color images is developed. The encryption process begins by transforming the image into a vector and generating chaotic keystreams, which are discretized into 8-bit integers. An initial diffusion is applied via a XOR operation, followed by a robust bidirectional diffusion process that propagates changes throughout the entire image. Security is further strengthened by a final index-based permutation stage that thoroughly scrambles the pixel positions, making the cipher-image highly resistant to cryptanalysis. Experimental results demonstrate enhanced security, positioning the system as a suitable tool for nonlinear dynamics analysis and cryptographic applications.
