Fixed-time synchronization for complex-valued BAM neural networks with time-varying delays via pinning control and adaptive pinning control

The paper mainly studies the fixed-time synchronization of complex-valued BAM neural networks with time-varying delays via pinning control and adaptive pinning control. Firstly, the pinning control mechanism is designed to merely control partial nodes but not all nodes, which not only saves resources, but also improves the communication efficiency. Then, based on the appropriate Lyapunov function and some basic inequality techniques, a new fixed-time synchronization criterion through pinning control method is derived. Secondly, in order to reduce the computational burden, an adaptive pinning controller is designed by combining pinning and adaptive control, which improves the control performance and automatically adjust the control parameters, and new sufficient condition of the fixed-time synchronization under adaptive pinning control is obtained. Meanwhile, the upper bounds of the settling time are computed. Finally, two numerical examples show the effectiveness and feasibility of our results.