Dynamics and synchronization of quantum cellular neural networks via manifold technology

This work solves the problem of maintaining consistency of robust connections for four-order quantum cellular neural networks (QCNNs) with limited communication range. Considering the limited communication capabilities of neural networks in practical applications, this research presents an innovative method that involves incorporating quantum-dot cellular automata (QCA) designed to ensure continuous communication connections within a QCNN. Additionally, a generalized synchronization for two four-order QCNNs is designed via manifold technology. Following the Lyapunov theorem and the control theory, this research concludes that, under specific conditions, two QCNNs can obtain the consensus synchronization. Moreover, an advanced control method named a linear manifold control scheme is described to reduce the chattering phenomenon in synchronization. Numerical example demonstrates the effectiveness and advantage of the proposed approach.