Arbitrary preassigned‐time control for synchronization of memristive cell neural networks and image encryption application

Abstract This paper proposes an arbitrary preassigned‐time sliding mode control (SMC) scheme to achieve synchronization in six‐dimensional memristive cellular neural networks (6D‐MCNNs). First, a novel 6D‐MCNNs model is established by incorporating three flux‐controlled memristors. The chaotic characteristics of the system are confirmed through Lyapunov exponent spectra and bifurcation analysis. Then, a new SMC strategy integrated with a disturbance observer is developed by introducing an effective time‐varying function. A new lemma is also presented to derive the conditions for arbitrary preassigned‐time synchronization (PTS), which guarantees that the error system reaches the sliding surface and maintains sliding motion within a preset time. Notably, the settling times for both phases are independent of initial conditions and other design parameters. Finally, an image encryption algorithm is designed to demonstrate the application of PTS in 6D‐MCNNs. Numerical simulations and statistical evaluations are provided to validate the theoretical findings and illustrate the potential of the proposed method in enhancing communication security.