Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks

• Main Authors: Usa Humphries, Grienggrai Rajchakit, Pramet Kaewmesri, Pharunyou Chanthorn, Ramalingam Sriraman, Rajendran Samidurai, Chee Peng Lim
• Format: Article
• Language: English
• Published: MDPI AG 2020-05-01
• Series: Mathematics
• Subjects: global asymptotic stability; fractional-order; quaternion-valued; bidirectional associative memory; linear matrix inequality
• Online Access: https://www.mdpi.com/2227-7390/8/5/801

We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper. Whether the real and imaginary parts of quaternion-valued activation functions are expressed implicitly or explicitly, they are considered to meet the global Lipschitz condition in the quaternion field. New sufficient conditions are derived by applying the principle of homeomorphism, Lyapunov fractional-order method and linear matrix inequality (LMI) approach for the two cases of activation functions. The results confirm the existence, uniqueness and global asymptotic stability of the system’s equilibrium point. Finally, two numerical examples with their simulation results are provided to show the effectiveness of the obtained results.