Dynamics for a Type of Differential-Algebraic Complex-Valued Neural Networks with Delay

Abstract

In the article, we apply complex-valued neural networks (CVNNs) to differential-algebraic neural networks (DANNs) and establish a new type of differential-algebraic complex-valued neural network (DACVNN) with delay (DDACVNN). First of all, the focus of existence and uniqueness of the solution to DDACVNN is addressed. Additionally, a theorem of global exponential stability (GES) of DDACVNN is investigated. In particular, in the discussion of this article, there is no restriction on whether the activation function requires that the real and imaginary parts can be dissociated. Finally, we will give two examples, namely, the activation function can separate the real and imaginary parts, and the activation function cannot separate the real and imaginary parts, both of which can confirm the truth of the effectiveness of theoretical results.