A fractional-order Gaussian memristive system with controllable multi-scroll attractors and its application in image encryption

The generation of multi-scroll chaotic attractors in fractional-order memristive systems remains a theoretical challenge due to the lack of analytically tractable memductance models and an insufficient understanding of scroll-formation mechanisms under fractional dynamics. To address this gap, we propose a novel memristor model based on Gaussian functions that exhibits essential properties, including pinched hysteresis, non-volatility, and local activity. Embedding this memristor into a fractional-order Sprott-C system yields a fractional memristive N-scroll chaotic system. Using fractional-order linear stability theory, we uncover a geometric mechanism whereby each scroll originates from conditionally stable equilibrium points aligned with power-off plot crossings, thereby generalizing classical scroll-generation principles to fractional-order regimes. Comprehensive parametric studies also reveal how the fractional order, peak morphology, and coupling strength govern the system dynamics. The proposed model not only advances the theoretical design of multi-scroll chaos but also demonstrates promising applications in medical image encryption, where its complex dynamics enhance both clinical data security and image restoration accuracy.