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This article investigates the multistability and stabilization of fractional-order competitive neural networks (FOCNNs) with unbounded time-varying delays. By utilizing the monotone operator, several sufficient conditions of the coexistence of equilibrium points (EPs) are obtained for FOCNNs with concave–convex activation functions. And then, the multiple $\mu $ -stability of delayed FOCNNs is derived by the analytical method. Meanwhile, several comparisons with existing work are shown, which implies that the derived results cover the inverse-power stability and Mittag–Leffler stability as special cases. Moreover, the criteria on the stabilization of FOCNNs with uncertainty are established by designing a controller. Compared with the results of fractional-order neural networks, the obtained results in this article enrich and improve the previous results. Finally, three numerical examples are provided to show the effectiveness of the presented results. [ABSTRACT FROM AUTHOR]

This article addresses the multistability and attraction of fractional-order neural networks (FONNs) with unbounded time-varying delays. Several sufficient conditions are given to ensure the coexistence of equilibrium points (EPs) of FONNs with concave–convex activation functions. Moreover, by exploiting the analytical method and the property of the Mittag–Leffler function, it is shown that the multiple Mittag–Leffler stability of delayed FONNs is derived and the obtained criteria do not depend on differentiable time-varying delays. In particular, the criterion of the Mittag–Leffler stability can be simplified to M-matrix. In addition, the estimation of attraction basin of delayed FONNs is studied, which implies that the extension of attraction basin is independent of the magnitude of delays. Finally, three numerical examples are given to show the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, multiple $\psi $ -type stability of Cohen–Grossberg neural networks (CGNNs) with both time-varying discrete delays and distributed delays is investigated. By utilizing $\psi $ -type functions combined with a new $\psi $ -type integral inequality for treating distributed delay terms, some sufficient conditions are obtained to ensure that multiple equilibrium points are $\psi $ -type stable for CGNNs with discrete and distributed delays, where the distributed delays include bounded and unbounded delays. These conditions of CGNNs with different output functions are less restrictive. More specifically, the algebraic criteria of the generalized model are applicable to several well-known neural network models by taking special parameters, and multiple different output functions are introduced to replace some of the same output functions, which improves the diversity of output results for the design of neural networks. In addition, the estimation of relative convergence rate of $\psi $ -type stability is determined by the parameters of CGNNs and the selection of $\psi $ -type functions. As a result, the existing results on multistability and monostability can be improved and extended. Finally, some numerical simulations are presented to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]