Mittag-Leffler stability analysis of multiple equilibrium points in impulsive fractional-order quaternion-valued neural networks

Abstract

In this study, we investigate the problem of multiple Mittag-Leffler stability analysis for fractional-order quaternion-valued neural networks (QVNNs) with impulses. Using the geometrical properties of activation functions and the Lipschitz condition, the existence of the equilibrium points is analyzed. In addition, the global Mittag-Leffler stability of multiple equilibrium points for the impulsive fractional-order QVNNs is investigated by employing the Lyapunov direct method. Finally, simulation is performed to illustrate the effectiveness and validity of the main results obtained.

Robust stability analysis of impulsive quaternion-valued neural networks with distributed delays and parameter uncertainties

“…It should be noted that the activation function is continuous in this article, however, the discontinuous case in QVNNs is our coming consideration, which is of great importance in real applications of everyday life. Recently, some researchers investigated the Mittag-Leffler stability of multiple equilibrium points for fractional-order QVNNs with an impulsive term [33]. Other interesting Figure 1 The first part of the state trajectories for system (1) with parameters Figure 2 The second part of the state trajectories for system (1) with parameters work involves the Hopf bifurcation of a fractional-order octonion-valued neural networks with time delay [34].…”

“…This important work is a substantial extension of traditional integerorder neural networks, which provide us a new way to extend our work. Note that, in references [33] and [34], to obtain the corresponding results, the authors transform their QVNNs into several RVNNs or CVNNs from research methods. In this article, we obtain the dynamical behaviors of QVNNs directly using the basic properties of QVNNs, instead of converting them into complex-or real-valued system, which avoids the increase of system dimension.…”

“…; to study the existence, boundedness of equilibrium of a system, different types of stability, synchronization, and bifurcation of a neural network. The research scope has also been extended from integer-order neural networks to fractional-order neural networks [33,34]. Recently, in [35], the authors presented a delayed QVNN with parameter uncertainties and investigated the robust stability of the system.…”

Global Mittag–Leffler Stabilization of Fractional-Order BAM Neural Networks with Linear State Feedback Controllers

“…e definitions of Mittag-Leffler stability and generalized Mittag-Leffler stability are proposed in [12,13]. Subsequently, some investigations focus on Mittag-Leffler stability [14][15][16][17][18][19][20][21]. Global Mittag-Leffler stability and synchronization analysis of discrete fractional-order complexvalued neural networks with time delay are given in [14].…”

“…Global Mittag-Leffler stability and synchronization analysis of discrete fractional-order complexvalued neural networks with time delay are given in [14]. In [15], the global Mittag-Leffler stability of multiple equilibrium points for the impulsive fractional-order quaternionvalued neural networks is investigated by employing the Lyapunov method. In [16], sufficient conditions ensuring the existence, uniqueness, and global Mittag-Leffler stability of the solutions of the fractional-order coupled system on a network without strong connections are derived.…”