This paper mainly utilizes the nondecomposition method to examine a problem of polynomial synchronization for the quaternion-valued memristive neural networks. First, to avoid considering the “magnitude” of a quaternion, the nonreduced-order and nondecomposition methods are applied to maintain computational efficiency without introducing new variables. Then, under a simple controller, the system’s global polynomial synchronization is guaranteed by formulating a suitable Lyapunov functional and using quaternion properties. Finally, an illustrative numerical example is included to substantiate the conclusion.
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