Dynamic analysis of fractional-order quaternion-valued fuzzy memristive neural networks: Vector ordering approach

This paper addresses the problems of stabilization and synchronization control of the fractional-order quaternion-valued fuzzy memristive neural networks. By means of the contraction mapping theorem, the corresponding conditions are established for the existence and uniqueness of the equilibrium point (EP), subsequently, the corresponding stability analysis are proposed by two suitable controllers. What should be mentioned is that, a vector ordering approach is developed to determine the "magnitude" of two different quaternions, as a result, the closed convex hull proposed by quaternion connections can be easily derived. Finally, two simulation examples are utilized to illustrate the effectiveness of the proposed control method.