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

• Published in: Mathematics and computers in simulation Vol. 201; pp. 508 - 527
• Main Authors: Rajchakit, G., Sriraman, R., Lim, C.P., Unyong, B.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2022
• Subjects: Asymptotic stability; Clifford-valued neural network; Exponential stability; Lyapunov functional; Neutral delay; Asymptotic stability; Clifford-valued neural network; Lyapunov functional; Exponential stability; Neutral delay
• ISSN: 0378-4754
• DOI: 10.1016/j.matcom.2021.02.023

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.