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 μ -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.

This paper addresses the robust stability of recurrent neural networks (RNNs) with time-varying delays and input perturbation, where the time-varying delays include discrete and distributed delays. By employing the new ψ-type integral inequality, several sufficient conditions are derived for the robust stability of RNNs with discrete and distributed delays. Meanwhile, the robust boundedness of neural networks is explored by the bounded input perturbation andL1-norm constraint. Moreover, RNNs have a strong anti-jamming ability to input perturbation, and the robustness of RNNs is suitable for associative memory. Specifically, when input perturbation belongs to the specified and well-characterized space, the results cover both monostability and multistability as special cases. It is revealed that there is a relationship between the stability of neural networks and input perturbation. Compared with the existing results, these conditions proposed in this paper improve and extend the existing stability in some literature. Finally, the numerical examples are given to substantiate the effectiveness of the theoretical results.

This article mainly investigates the multiple Mittag-Leffler stability of delayed fractional-order Cohen-Grossberg neural networks with time-varying delays. By using mixed monotone operator pair, the conditions of the coexistence of multiple equilibrium points are obtained for fractional-order Cohen-Grossberg neural networks, and these conditions are eventually transformed into algebraic inequalities based on the vertex of the divided region. In particular, when the symbols of these inequalities are determined by the dominant term, several verifiable corollaries are given. And then, the sufficient conditions of the Mittag-Leffler stability are derived for fractional-order Cohen-Grossberg neural networks with time-varying delays. In addition, two numerical examples are provided to illustrate the effectiveness of the theoretical results.

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.

This paper investigates Cohen-Grossberg neural networks (CGNNs) with unbounded time-varying delays. The existence condition of multiple equilibrium points is established by the algebraic inequality method. And then, the ψ-type stability is studied by analysis method for CGNNs with unbounded time-varying delays, and the relative convergence rate can be adjusted by the selection of ψ-type functions. Moreover, by introducing the topological degree, the algebraic sum of the number of equilibria remains unchanged for any smooth function in the specified metric space. Finally, one numerical example is implemented to show the validity of the presented results.

This article deals with the asymptotic stability and synchronization of fractional-order neural networks (FONNs) with unbounded time-varying delays, in which FONNs can be the general nonlinear system. First, the existence of the equilibrium point of the nonlinear system is obtained, and the μ-type stability of fractional-order nonlinear systems is proved by the analytical method. Second, several sufficient conditions are derived to guarantee the μ-type stability of FONNs by taking easily implemented parameters. Moreover, the μ-type synchronization of drive-response systems is established by designing the linear controller. Especially, μ-type stability is the general stability, including Mittag-Leffler stability and power-stability, which is the extension of the Mittag-Leffler stability of FONNs. Finally, two numerical examples are presented to show the effectiveness of the results.

This paper is concerned with multiple Lagrange stability under perturbation for recurrent neural networks with time-varying delays. This is different from traditional Lagrange stability, which means that multiple Lagrange stability under perturbation holds for any disturbance of initial value and any structural perturbation, within a specified and well-characterized set. In this paper, multiple Lagrange stability under perturbation with respect to a finite number of trivial solutions is established, which has good robustness. Under certain perturbation, the core of the proof of the boundedness of trajectories in mutually disjoint subregions is to employ the generalized differential inequality. The results supplement and extend some previous results, and they are applicable to robust analysis of multiple equilibria. Finally, numerical calculation and simulations are implemented to illustrate the effectiveness of the theoretical results.

In this paper, the ψ -type stability and robustness of recurrent neural networks are investigated by using the differential inequality. By utilizing ψ -type functions combined with the inequality techniques, some sufficient conditions ensuring ψ -type stability and robustness are derived for linear neural networks with time-varying delays. Then, by choosing appropriate Lipschitz coefficient in subregion, some algebraic criteria of the multiple ψ -type stability and robust boundedness are established for the delayed neural networks with time-varying delays. For special cases, several criteria are also presented by selecting parameters with easy implementation. The derived results cover both ψ -type mono-stability and multiple ψ -type stability. In addition, these theoretical results contain exponential stability, polynomial stability, and μ -stability, and they also complement and extend some previous results. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed criteria.

In this paper, multiple ψ -type stability of Cohen-Grossberg neural networks (CGNNs) with both time-varying discrete delays and distributed delays is investigated. By utilizing ψ -type functions combined with a new ψ -type integral inequality for treating distributed delay terms, some sufficient conditions are obtained to ensure that multiple equilibrium points are ψ -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 ψ -type stability is determined by the parameters of CGNNs and the selection of ψ -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.