Fixed-time synchronization of time-varying coupled competitive neural networks with impulsive effects

This paper investigates the problem of fixed-time synchronization of time-varying coupled competitive neural networks with impulsive effects. Synchronizing impulses and desynchronizing impulses are each taken into account. The innovative pure power-law control is designed in this paper to avoid vibratory behaviors, which is more straightforward and effective than the common design including the linear and power-law terms. Note that the key difficulty is determining how to ensure fixed-time synchronization and estimate the settling time in an impulsive sense since the impulsive influences may lead to the discontinuity of the states. However, the theoretical framework of fixed-time synchronization under desynchronizing impulses has not been constructed much in the existing literature, which deeply motivated us to contribute to this analysis. By using the average impulsive intervals method, graph theory, and the Lyapunov method, two cases of the settling time along with the fixed-time synchronization criteria regarding the synchronizing and desynchronizing impulses are given. Lastly, a numerical example is provided to show the viability and accuracy of the discovered theoretical results.