Fixed-time synchronization of delayed memristive neural networks with impulsive effects via novel fixed-time stability theorem.

In this study, the fixed-time synchronization (FXTS) of delayed memristive neural networks (MNNs) with hybrid impulsive effects is explored. To investigate the FXTS mechanism, we first propose a novel theorem about the fixed-time stability (FTS) of impulsive dynamical systems, where the coefficients are extended to functions and the derivatives of Lyapunov function (LF) are allowed to be indefinite. After that, we obtain some new sufficient conditions for achieving FXTS of the system within a settling-time using three different controllers. At last, to verify the correctness and effectiveness of our results, a numerical simulation was conducted. Significantly, the impulse strength studied in this paper can take different values at different points, so it can be regarded as a time-varying function, unlike those in previous studies (the impulse strength takes the same value at different points). Hence, the mechanisms in this article are of more practical applicability. • Novel fixed-time stability theorem with indefinite derivative of Lyapunov function. • Impulse strength can take different values at different impulse points. • New fixed-time synchronization mechanisms via three different controllers. • Settling time is related to the selection of the impulse points and the impulse strength. [ABSTRACT FROM AUTHOR]