Abstract
AbstractThis chapter concentrates on the fixed-time pinning synchronization and adaptive synchronization problems of complex-valued inertial neural networks (CVINNs) with time-varying delays. We will regard this model as an entirety instead of reducing it to first-order differential equation, separate the real and imaginary parts into an equivalent real-valued one, and establish 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. Moreover, from the point of saving cost and avoiding resources waste, we will continue to further develop a new pinning adaptive controller and derive a sufficient condition ensuring the adaptive fixed-time stability for the closed-loop error system.
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