Abstract
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.
Highlights
Many analyses pertaining to the dynamical behaviors of different classes of neural network (NN) models have been reported in the literature
We have investigated the FQVBAMNN models with respect to its existence, uniqueness and global asymptotic stability
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, which ensure the existence, uniqueness, and globally asymptotic stability of the equilibrium point of the considered system model
Summary
Many analyses pertaining to the dynamical behaviors of different classes of neural network (NN) models have been reported in the literature. Based on new Lyapunov functional and some inequality techniques, global synchronization conditions were derived for fractional-order QVNNs in Reference [36]. In Reference [40], the problem of global Mittag-Leffler stability and stabilization has been investigated for fractional-order quaternion-valued memristive NNs by using the real-imaginary separate method. The fractional-order QVNN model was analyzed in Reference [41], in which issues related to synchronization and global Mittag-Leffler stability were tackled. By use of new fractional-order inequality as well as the Lyapunov fractional-order method, the global Mittag-Leffler synchronization problem pertaining to FQVBAMNN models was studied in Reference [13]. To reduce the complexity in calculations of fractional-order QVNNs, the decomposition method was used to the problem of finite-time Mittag-Leffler stability in Reference [52].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
