Fixed-time synchronization of inertial complex-valued neural networks with time delays

This paper studies the problem of fixed-time synchronization for a class of delayed complex-valued neural networks with inertial term. Two different controllers are designed, under which the addressed inertial complex-valued neural networks with different types of activation functions can achieve synchronization perfectly in a fixed time. The corresponding synchronization criteria in terms of matrix inequalities and the estimates of the settling times are derived by using separation and direct methods, respectively, which are concise and easy to verify compared with algebraic inequalities conditions. Some innovative inequalities in the complex field are fully utilized. The in-depth analysis results are an advancement of the existing research progress. Finally, in order to support the theoretical results, numerical simulations for different types of activation functions are provided.