Fixed-time synchronization of fractional order memristive MAM neural networks by sliding mode control

In this paper, we first established the fractional order memristive multidirectional associative memory neural networks (FMMAMNNs) model, and then considered its fixed-time synchronization control problem. On the basis of sliding model control and Lyapunov stability theorem, a fractional order sliding mode controller is constructed. By adding this controller to the response system, the error of the driver-response systems gradually converges to 0 in a fixed time. Compared with the previous researches, this paper considers a more complex model, and the proposed control theories can ensure that the setting time is only related to the model and controller, but not to the initial states of the system. Besides, the control theories are also applicable to the integer order models. Finally, two numerical simulations are given, the results show the validity of the theories.