Improved fixed-time sliding mode synchronization control of a new 4-cell memristive CNN chaotic system with the offset boosting via certain self-parameters

A new 4-cell memristive cellular neural network (CNN) is proposed, in which a current-controlled generic memristor substitutes the resistor in one cell’s output. Within the CNN system, various dynamic behaviors are generated, including symmetrical and asymmetrical double-wing chaotic attractors, single-wing chaotic attractors, and periodic attractors, resulting from bifurcation phenomena with two memristor parameters varying. More interestingly, the remaining two memristor parameters pose partially amplitude control and offset boosting to the variables or dynamics of the CNN system, due to no bifurcation phenomena by varying them. The theoretical findings are validated by circuit realization. Moreover, an improved sliding mode synchronization control for the proposed CNN system with external disturbance and non-modeled dynamics is introduced. Under the sliding mode control, the responsive system in the secure communication can achieve synchronization with the driving system, both of which are specified by the proposed CNN system. The synchronization time is fixed and independent of their initial conditions. The synchronization control strategy is robust in a degree, as the synchronization is achieved and the synchronization times are nearly indistinguishable for CNNs both with and without disturbances and non-modeled dynamics, while solving the problem of chattering. Moreover, the synchronization time can be shorten by parameters of the sliding mode surface and the controller, as well as the parameter of the additional term through decreasing the overshoot of the convergence process of the synchronization error system. Finally, all the performances are validated by numerical simulations. The research findings pave a way for future applications to secure communications.