Anti-periodic Synchronization of Quaternion-valued Generalized Cellular Neural Networks with Time-varying Delays and Impulsive Effects

In this paper, a class of quaternion-valued generalized cellular neural networks (QVGCNNs) with time-varying delays and impulsive effects is considered. Firstly, by constructing an appropriate Lyapunov function and applying inequality techniques, some sufficient conditions on the existence of anti-periodic solutions are established. Then, the global exponential anti-periodic synchronization of delayed QVGCNNs with impulsive effects and anti-periodic coefficients is investigated by designing a novel nonlinear state-feedback controller and constructing suitable Lyapunov functions. Our results are completely new even if the considered quaternion-valued systems degenerated into real-valued or complex-valued systems. Finally, two numerical examples are given to illustrate the feasibility and effectiveness of the obtained results.