Abstract
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 M-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.
Highlights
Research in the past decades have shown that neural networks (NNs) have a wide range of applications in many fields as detection and analysis of the biological signal, image processing, system control, and so on
Given the foregoing discussion, this paper focuses on developing a new direct quaternionic method to research the global exponential stability (GES) of a class of multiple time-varying delayed memristive quaternionic neural networks (MQNNs)
We will first prove that the below matrix equation has a unique quaternionic solution p∗ to demonstrate that (7) holds an equilibrium solution (ES)
Summary
Research in the past decades have shown that neural networks (NNs) have a wide range of applications in many fields as detection and analysis of the biological signal, image processing, system control, and so on. It is of great significance to introduce memristors into neural network design and to study memristive neural networks [3,4,5,6,7]. Due to the switching speed of the amplifier and the transmission delay during communication between neurons, it is necessary to introduce time delays when designing neural networks. It is widely known that stability is a prerequisite for the good application of a system. It is important to study the stability of neural network systems with time delays [1,2,3]
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