Novel Criteria of Stability for Delayed Memristive Quaternionic Neural Networks: Directly Quaternionic Method

• Main Authors: Jie Pan, Lianglin Xiong
• Format: Article
• Language: English
• Published: MDPI AG 2021-06-01
• Series: Mathematics
• Subjects: memristive quaternionic neural networks (MQNN); global exponential stability (GES); time-varying delay; <i>M</i>-matrix
• Online Access: https://www.mdpi.com/2227-7390/9/11/1291

In this paper, we fixate on the stability of varying-time delayed memristive quaternionic neural networks (MQNNs). With the help of the closure of the convex hull of a set the theory of differential inclusion, MQNN are transformed into variable coefficient continuous quaternionic neural networks (QNNs). The existence and uniqueness of the equilibrium solution (ES) for MQNN are concluded by exploiting the fixed-point theorem. Then a derivative formula of the quaternionic function’s norm is received. By utilizing the formula, the <i>M</i>-matrix theory, and the inequality techniques, some algebraic standards are gained to affirm the global exponential stability (GES) of the ES for the MQNN. Notably, compared to the existing work on QNN, our direct quaternionic method operates QNN as a whole and markedly reduces computing complexity and the gained results are more apt to be verified. The two numerical simulation instances are provided to evidence the merits of the theoretical results.