Quasi-stability and quasi-synchronization control of quaternion-valued fractional-order discrete-time memristive neural networks

Highlights：

• We make the first attempt to study the quaternion-valued fractional-order discrete-time memristive neural networks.

• In this paper, the error system tends to a region as time goes to infinity, which is much more reasonable in practical.

• Instead of separating the system into real part and imaginary part, in this paper, a direct approach is employed to deal with the quaternion-valued memristive neural networks, which is much more tally with the actual.

• A lexicographical order method is employed in this paper, which can be used to determine the “magnitude” of any two different quaternions. Moreover, based on the proposed method, the dynamic behaviors of the complex-valued (or quaternion-valued) neural networks with interval parameters can also be studied.