Tunable Dynamics of Memristive Chaotic Systems and Its Application in Water Facility Image Encryption

Nonlinear memristors frequently contribute to enhancing the dynamical richness of chaotic systems, yet their complexity and flexibility have often been overlooked. In this work, a piecewise non-smooth threshold memristor model is proposed, which is coupled as a nonlinear term into the Sprott C system, yielding a novel four-dimensional memristive chaotic dynamical system. From a theoretical perspective, stability analysis reveals that unstable index-2 saddle-focus equilibrium points are governed by the memristive piecewise parameter, and the topological invariance of the system is verified. In numerical simulations, bifurcation diagrams, Lyapunov exponents, and phase portraits are employed to reveal the mechanism of novel tunable chaotic dynamics. The results demonstrate that memristive coupling strength can induce the system to generate double-scroll, double-wing, and double-butterfly chaotic attractors; the piecewise parameter of the memristor can control the system to produce multi-structure attractors with expanded quantity, and the initial condition of the memristor can regulate the system to generate offset-boosted chaotic attractors. Finally, the novel tunable dynamics is applied to water facility image encryption. Experimental results demonstrate that the proposed algorithm possesses a key space of 2100, a correlation coefficient of only 0.0002, and information entropy close to the ideal value of eight. The NPCR and UACI reach 99.6161% and 33.4669%, respectively, the key sensitivity is up to 10−16, and all p-values from the NIST tests are greater than 0.01, confirming that the algorithm achieves excellent security performance.