Projective synchronization of fractional order quaternion valued uncertain competitive neural networks

Abstract

In this manuscript, we investigate the projective synchronization (PS) of fractional-order quaternion-valued uncertain competitive neural networks (FQVUCNNs). First, we construct quaternion-valued adaptive control and use this control to ensure the realization of asymptotic adaptive projective synchronization (AAPS) for FQVUCNNs. Also, we examine finite-time projective synchronization (FTPS) of the FQVUCNNs using quaternion-valued feedback control. Instead of using the usual decomposition technique, we treat the quaternion-valued state as a single entity and establish the synchronization criteria for FQVUCNNs using the Lyapunov direct method and the properties of fractional derivatives. Further, the practical viability and effectiveness of the theoretical findings are demonstrated through an illustrative example, underlying the significance of this research.