Pinning synchronization and adaptive synchronization of complex-valued inertial neural networks with time-varying delays in fixed-time interval

This article concentrates on pinning synchronization and adaptive synchronization problems of complex-valued inertial neural networks with time-varying delays in fixed-time interval. First, regarding complex-valued inertial neural networks model as an entirety instead of reducing this system to first-order differential equation, separating the real and imaginary parts of this system into an equivalent real-valued one, and establishing a novel Lyapunov function, the fixed-time stability for the closed-loop error system is guaranteed via partial nodes controlled directly by a new pinning controller which involves the state derivatives and other proper terms. Then, from the point of saving cost and avoiding resources waste, a new pinning adaptive controller is further developed and sufficient condition ensuring the adaptive fixed-time stability for the closed-loop error system is also derived. In the end, the effectiveness of these results is verified by a numerical example.