Polynomial synchronization of quaternion-valued fuzzy cellular neural networks with proportional delays

This paper mainly utilizes the non-decomposition method to examine a problem of polynomial synchronization for the quaternion-valued fuzzy cellular neural networks with proportional delays. Firstly, we prove a lemma explaining the solution form of a quaternion-valued differential system. Furthermore, under the Banach fixed point theory and some scaling techniques, we prove that this system’s unique almost periodic solution exists in the specific closed convex subset. Secondly, depending on the infinite norm of the quaternion-valued vector, the Lyapunov functional is formulated without time delay. Besides, the global polynomial synchronization of the whole quaternion-valued system is investigated by constructing a suitable nonlinear controller and exploiting the properties of quaternions and related inequalities. Ultimately, an illustrative numerical example is included to substantiate the conclusion.