Mittag-Leffler stability of fractional-order quaternion-valued memristive neural networks with generalized piecewise constant argument.

This paper studies the global Mittag-Leffler (M-L) stability problem for fractional-order quaternion-valued memristive neural networks (FQVMNNs) with generalized piecewise constant argument (GPCA). First, a novel lemma is established, which is used to investigate the dynamic behaviors of quaternion-valued memristive neural networks (QVMNNs). Second, by using the theories of differential inclusion, set-valued mapping, and Banach fixed point, several sufficient criteria are derived to ensure the existence and uniqueness (EU) of the solution and equilibrium point for the associated systems. Then, by constructing Lyapunov functions and employing some inequality techniques, a set of criteria are proposed to ensure the global M-L stability of the considered systems. The obtained results in this paper not only extends previous works, but also provides new algebraic criteria with a larger feasible range. Finally, two numerical examples are introduced to illustrate the effectiveness of the obtained results.