Fixed/predefined-time synchronization of memristive neural networks based on state variable index coefficient

This paper has investigated the fixed/predefined-time synchronization problem of delayed memristive neural networks(DNNs). Firstly, two novel controllers with state variable index coefficient are presented for achieving fixed-time synchronization of driver-response systems. Then, one effective control scheme is proposed out to realize predefined-time synchronization based on the results of fixed-time synchronization. Meanwhile, some conditions are given to direct how to select suitable controllers' parameters by employing fixed-time and Lyapunov theory. The established control schemes are shown to have simpler structures and may need lower energy. In addition, the settling time of fixed time synchronization has been estimated independently on initial states while predefined-time can be set by user in advance. At last, numerical experiments are conducted to verify the effectiveness of the results.