A novel fixed-time stability result and its application to synchronization of delayed multidirectional associative memory neural networks with discontinuous activations.

In this paper, in order to realize time-saving and low-consumption secure communication based on fixed-time (FXT) synchronization, some new FXT stability results and a smaller upper bound of settling time are obtained by using inequality techniques, variable substitution method and some special functions, including beta function and incomplete beta function. Moreover, the FXT synchronization of delayed multidirectional associative memory (MAM) neural networks with discontinuous activations is investigated by employing the differential inclusion theory, the improved FXT stability theorem and a simple delay-independent nonlinear controller. Finally, a numerical simulation is given to verify the correctness of the theoretical results and the effectiveness of FXT synchronization in secure communication. The results show that the upper bound estimation of settling time in this paper is indeed smaller than that in some previous researches. In addition, the encrypted signals can be quickly decrypted based on the improved FXT stability results, but may not be decrypted by the existing FXT stability results.