Quantized projective synchronization of discrete‐time fractional‐order delayed quaternion‐valued fuzzy neural networks and its application to image encryption

In this paper, we address the projective synchronization (PS) of discrete‐time fractional‐order delayed quaternion‐valued fuzzy neural networks (DFDQFNNs), which is solved by a nondecomposition method. Initially, a DFDQFNN system is established. Following this, this work presents a quantized controller that employs a sign function within the quaternion framework, which conserves channel resources and reduces control costs. Furthermore, by means of ‐difference theory and the effective quantized controller as well as inequality techniques, some sufficient criteria have been earned to ensure the PS of DFDQFNNs. Ultimately, the theoretical contributions of this paper are validated through rigorous numerical simulations.