Projective Synchronization of Quaternion-Valued Discontinuous Competitive Neural Networks with Multiple Time Scales

Article Projective Synchronization of Quaternion-Valued Discontinuous Competitive Neural Networks with Multiple Time Scales Yu Zheng, Ruoyu Wei * and Zixuan Chen School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China * Correspondence: [email protected] Received: 28 March 2025; Revised: 18 April 2025; Accepted: 22 April 2025; Published: 24 April 2025 Abstract: In this study, we explore the projective synchronization of quaternion-valued competitive neural networks with multiple time scales (QVMTSCNNs), while analyzing the impacts of discontinuous activation functions and time delays. To achieve the control goal, two novel quaternion controllers are designed, which do not depend on the ratio of the fast and slow time scales. By applying the nonsmooth analysis and quaternion inequality techniques, two novel theorems for projective synchronization of QVMTSCNNs are derived by non-separating methods. The obtained results in this study are relatively simpler and straightforward, extending some previous findings. Lastly, numerical analyses are executed to substantiate the theoretical conclusions.