Constructing multiscroll multistability in the Duffing oscillator with application to urban architectural image security

The central challenge in urban architectural image security lies not in generating chaos itself, but in extracting sufficiently diverse keystreams from nonlinear dynamical systems. To break this bottleneck, a hierarchically nested memristor is bidirectionally coupled with the classical Duffing oscillator, which offers a canonical reduced-order representation of nonlinear vibration in structural systems, to form a four-dimensional autonomous memristive Duffing system. The nested nonlinearity combines absolute-value folding, sign-preserving transformation, and multilevel offset boosting. The nesting depth expands the multiscroll capacity, while the level-dependent offsets regulate attractor number, spatial location, adjacent spacing, and coexistence morphology. A digital hardware implementation reproduces multiscroll states and coexisting phase trajectories, validating the physical realizability of the proposed system. Finally, distinct coexisting-attractor trajectories are incorporated into a key-separated image encryption framework using HKDF/HMAC-SHA256, separating dynamical-state diversity from cryptographic unpredictability, with effectiveness verified on urban architectural images.