The main objective of this paper is to design an aperiodically intermittent control to ensure the finite and fixed time synchronization of fuzzy cellular neural networks (FCNNs) involving switching parameters with threshold properties, time-dependent discrete, continuous-type delays, and stochastic disturbances during transmission. Cellular neural networks (CNNs), with their grid-like structure, excel in image-processing tasks. Incorporating the fuzziness in the CNNs may handle the uncertainties and incomplete information in an effective manner. Furthermore, this paper introduces the concept of user-controlled FCNNs, which retain the dynamic properties of conventional FCNNs while incorporating significant factors that could potentially degrade the performance of the considered model. Due to randomness, FCNNs are framed as a set of stochastic differential equations with memristors. Generally, a memristor functions as a non-volatile memory device, reserving past data and utilizing it in the event of transmission failure. Further, the synchronization process is an effective approach that helps to ensure the dynamical behaviors of two different models; hence, the paper formulates the synchronization problem for the FCNN model with control (response) and without control input (drive). In terms of control design, this paper also considers the aperiodically intermittent control (APIC) scheme that can drive the user-controlled FCNN solution trajectories onto conventional FCNN solution trajectories within a prescribed time. Additionally, the APIC scheme incorporates an adaptive mechanism that effectively manages switching behaviors and uncertainties. Furthermore, this study proposes a theoretical framework in the form of sufficient stability conditions that helps to ensure the synchronization of the drive-response model via the global asymptotical stability of the stochastic error model derived from the drive-response model under the APIC scheme in the mean square. The proposed stochastic FCNN model is numerically simulated, and the corresponding outcomes are graphically illustrated.
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