Uniform Stability of Complex-Valued Neural Networks of Fractional Order With Linear Impulses and Fixed Time Delays

New delay-dependent uniform stability criteria for fractional-order BAM neural networks with discrete and distributed delays

Initially, a class of Caputo fractional-order bidirectional associative memory neural networks in two variables is developed, building upon the groundwork laid by delayed Caputo fractional system in one variable. Next, the Razumikhin-type uniform stability conditions, originally formulated for single-variable systems, are successfully extended to accommodate the complexities of delayed Caputo fractional systems in two variables. Leveraging this extension and employing a suitable Lyapunov function, the delay-dependent uniform stability criteria for the addressed fractional-order bidirectional associative memory neural networks are expressed in terms of linear matrix inequalities. Finally, the effectiveness and practicality of the theoretical findings are demonstrated through the application of two numerical examples, affirming the viability of the proposed approach.

Global synchronization of complex-valued neural networks with unbounded time-varying delays

This paper investigates global synchronization of complex-valued neural networks (CVNNs) with unbounded time-varying delays. By applying analytical method and inequality techniques, an algebraic criterion is established to ensure global synchronization of the CVNNs via a devised feedback controller, which generalizes some existing outcomes. Finally, two numerical simulations and one application in image encryption are provided to verify the effectiveness of the theoretical results.

Fractional dynamic analysis and optimal control problem for an SEIQR model on complex networks

A fractional order susceptible-exposed-infected-quarantined-recovered model is established on the complex networks. We calculate a specific expression for the basic reproduction number R₀, prove the existence and uniqueness with respect to the solution, and prove the Ulam-Hyers stability of the model. Using the Latin hypercube sampling-partial rank correlation coefficient method, the influence of parameters on the R₀ is analyzed. Based on the results of the analysis, the optimal control of the model is investigated as the control variables with vaccination rate and quarantine rate applying Pontryagin's minimum principle. The effects of α, degree of nodes, and network size on the model dynamics are simulated separately by the prediction correction method.

Uniform Stability of a Class of Fractional-Order Fuzzy Complex-Valued Neural Networks in Infinite Dimensions

In this paper, the problem of the uniform stability for a class of fractional-order fuzzy impulsive complex-valued neural networks with mixed delays in infinite dimensions is discussed for the first time. By utilizing fixed-point theory, theory of differential inclusion and set-valued mappings, the uniqueness of the solution of the above complex-valued neural networks is derived. Subsequently, the criteria for uniform stability of the above complex-valued neural networks are established. In comparison with related results, we do not need to construct a complex Lyapunov function, reducing the computational complexity. Finally, an example is given to show the validity of the main results.

Global Mittag-Leffler stability and existence of the solution for fractional-order complex-valued NNs with asynchronous time delays

This paper is dedicated to exploring the global Mittag-Leffler stability of fractional-order complex-valued (CV) neural networks (NNs) with asynchronous time delays, which generates exponential stability of integer-order (IO) CVNNs. Here, asynchronous time delays mean that there are different time delays in different nodes. Two new inequalities concerning the product of two Mittag-Leffler functions and one novel lemma on a fractional derivative of the product of two functions are given with a rigorous theoretical proof. By utilizing three norms, several novel conditions are concluded to guarantee the global Mittag-Leffler stability and the existence and uniqueness of an equilibrium point. Considering the symbols of the matrix elements, the properties of an M-matrix are extended to the general cases, which introduces the excitatory and inhibitory impacts on neurons. Compared with IOCVNNs, exponential stability is the special case of our results, which means that our model and results are general. At last, two numerical experiments are carried out to explain the theoretical analysis.