LAGRANGE SYNCHRONIZATION OF HIGHER-DIMENSIONAL COHEN–GROSSBERG NEURAL NETWORKS WITH INTERACTION TERMS AND DISCRETE AND DISTRIBUTED TIME DELAYS

This paper examines the Lagrange synchronization of nonidentical higher-dimensional neural networks, particularly for the Cohen Grossberg octonion-valued neural networks (CGOVNNs) with interaction terms, time-varying, and distributed delays. Achieving synchronization in such systems is extremely difficult since the octonion algebra is non-commutative and non-associative. To address this, the Octonion valued neural network (OVNN) is first split into eight real-valued subsystems, which makes an organized analytical approach possible. A nonlinear controller is developed to guarantee synchronization, and an appropriate Lyapunov function is constructed. The sufficient requirements for Lagrange synchronization using the Lyapunov stability theory are proved. The efficacy of the suggested method is confirmed by numerical simulations. These results shed light on the synchronization of hypercomplex systems and aid in the stability study of high-dimensional neural networks.