Existence, uniqueness and global stability of Clifford-valued neutral-type neural networks with time delays

In this paper, we analyze the global asymptotic stability and global exponential stability with respect to the Clifford-valued neutral-type neural network (NN) models with time delays. By considering the neutral term, a Clifford-valued NN model with time delays is formulated, which encompasses real-valued, complex-valued, and quaternion-valued NN models as special cases. In order to achieve our main results, the n-dimensional Clifford-valued NN model is decomposed into 2mn-dimensional real-valued models. Moreover, a proper function is constructed to handle the neutral term and prove that the equilibrium point exists. Utilizing the homeomorphism theory, linear matrix inequality as well as Lyapunov functional methods, we derive the sufficient conditions corresponding to the existence, uniqueness, and global asymptotic stability with respect to the equilibrium point of the Clifford-valued neutral-type NN model. Numerical examples to demonstrate the effectiveness of the results are provided, and the simulations results are analyzed and discussed. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This paper analyzes the global asymptotic stability and global exponential stability of Clifford-valued neutral-type neural network models with time delays. By considering the neutral term, a Clifford-valued neural network model with time delays is formulated, encompassing real-valued, complex-valued, and quaternion-valued neural network models as special cases. With the decomposition of the n-dimensional Clifford-valued neural network model into 2mn-dimensional real-valued models, a proper function is constructed to handle the neutral term and prove the existence of the equilibrium point. By utilizing homeomorphism theory, linear matrix inequality, and Lyapunov functional methods, sufficient conditions for the existence, uniqueness, and global asymptotic stability of the equilibrium point for the Clifford-valued neutral-type neural network model are derived. Numerical examples are provided to demonstrate the effectiveness of the results, and the simulation results are analyzed and discussed.