A fixed-time sliding mode control scheme for synchronizing memristor-based four-dimensional hyperchaotic systems

Abstract Memristive hyperchaotic systems have attracted considerable attention in nonlinear dynamics and secure communications owing to their complex dynamical behaviors and hardware implementability. However, existing memristive chaotic systems suffer from limited attractor complexity, and the synchronization controllers designed for such systems frequently encounter singularity issues, finite settling-time dependence on initial conditions, and excessive chattering under external disturbances. In this paper, a four-dimensional hyperchaotic system is constructed by incorporating a smooth quadratic memristor into the Sprott-A framework, whose chaotic behaviors are validated through numerical simulations, Multisim circuit simulations, and FPGA hardware experiments; moreover, a φ -function-based fixed-time sliding mode controller with a time-varying integral sliding surface is proposed, which eliminates the reaching phase, avoids singularity, and achieves disturbance-robust synchronization with an initial-condition-independent convergence bound, as confirmed by Lyapunov stability analysis and comparative experiments. The proposed system and controller provide a theoretically rigorous and hardware-verified foundation for the design of high-security chaotic encryption and real-time synchronization systems.