Non-autonomous Neural Networks Research Articles

Finite-time contractive stability for fractional-order nonlinear systems with delayed impulses: Applications to neural networks

This paper deals with finite-time stability (FTS) and finite-time contractive stability (FTCS) criteria of fractional-order nonlinear systems (FONSs), where the state of the systems consists of a finite number of delayed impulsive instants. To achieve these results, we have extended the theories on FTS and FTCS criteria from integer-order NSs to fractional-order systems. Employing the fractional-order Lyapunov stability theory, the sufficient conditions of the above-mentioned stability criteria are derived for a class of FONSs with state-dependent delayed impulses. Then, to ensure the applicability of the proposed results, we have analyzed the desired performances for several neural network (NN) models, such as non-autonomous NNs (NANNs), Cohen–Grossberg NNs (CGNNs), switched NNs (SNNs) and bidirectional associative memory NNs (BAMNNs). Finally, four representative numerical examples are illustrated to demonstrate the assurance of the obtained stability conditions of the respective state-dependent impulsive fractional-order NNs (FONNs).

Generalized Halanay Inequalities and Asymptotic Behavior of Nonautonomous Neural Networks with Infinite Delays

This paper focuses on the asymptotic behavior of nonautonomous neural networks with delays. We establish criteria for analyzing the asymptotic behavior of nonautonomous recurrent neural networks with delays by means of constructing some new generalized Halanay inequalities. We do not require to constructi any complicated Lyapunov function and our results improve some existing works. Lastly, we provide some illustrative examples to demonstrate the effectiveness of the obtained results.

Exponential Stability of Impulsive Timescale-Type Nonautonomous Neural Networks With Discrete Time-Varying and Infinite Distributed Delays.

Global exponential stability (GES) for impulsive timescale-type nonautonomous neural networks (ITNNNs) with mixed delays is investigated in this article. Discrete time-varying and infinite distributed delays (DTVIDDs) are taken into consideration. First, an improved timescale-type Halanay inequality is proven by timescale theory. Second, several algebraic inequality criteria are demonstrated by constructing impulse-dependent functions and utilizing timescale analytical techniques. Different from the published works, the theoretical results can be applied to GES for ITNNNs and impulsive stabilization design of timescale-type nonautonomous neural networks (TNNNs) with mixed delays. The improved timescale-type Halanay inequality considers time-varying coefficients and DTVIDDs, which improves and extends some existing ones. GES criteria for ITNNNs cover the stability conditions of discrete-time nonautonomous neural networks (NNs) and continuous-time ones, and these theoretical results hold for NNs with discrete-continuous dynamics. The effectiveness of our new theoretical results is verified by two numerical examples in the end.

An improved fixed-time stabilization problem of delayed coupled memristor-based neural networks with pinning control and indefinite derivative approach

<abstract><p>In this brief, we propose a class of generalized memristor-based neural networks with nonlinear coupling. Based on the set-valued mapping theory, novel Lyapunov indefinite derivative and Memristor theory, the coupled memristor-based neural networks (CMNNs) can achieve fixed-time stabilization (FTS) by designing a proper pinning controller, which randomly controls a small number of neuron nodes. Different from the traditional Lyapunov method, this paper uses the implementation method of indefinite derivative to deal with the non-autonomous neural network system with nonlinear coupling topology between different neurons. The system can obtain stabilization in a fixed time and requires fewer conditions. Moreover, the fixed stable setting time estimation of the system is given through a few conditions, which can eliminate the dependence on the initial value. Finally, we give two numerical examples to verify the correctness of our results.</p></abstract>

Fixed-time synchronization problem of coupled delayed discontinuous neural networks via indefinite derivative method

<abstract><p>In this brief, we introduce a class of coupled delayed nonautonomous neural networks (CDNNs) with discontinuous activation function. Different from the conventional Lyapunov method, this brief uses the implementation of an indefinite derivative to deal with the nonautonomous system for the case that the topology between neurons is nonlinear coupling, and the system can achieve synchronization in fixed time by selecting the suitable control scheme. The settling time estimation of the system which can get rid of the dependence on the initial value is given. Finally, two examples are given to verify the correctness of the results in this paper.</p></abstract>

Exponential stability criteria for linear neutral systems with applications to neural networks of neutral type

Linear neutral vector equationsx˙(t)=A0(t)x˙(h0(t))+∑k=1mAk(t)x(hk(t))+∫g(t)tP(t,s)x(s)dsare considered on interval [0,∞). Here x=(x1,…,xn)T, m is a positive integer, the entries of matrices Al, l=0,…,m, P, and the delays hk, k=0,…,m, g are assumed to be Lebesgue measurable functions. New explicit criteria are derived on uniform exponential stability. Comparisons are made and discussed based on an overview of the existing results. An application is presented to local exponential stability of non-autonomous neural network models of neutral type.

Synchronization of nonautonomous neural networks with Caputo derivative and time delay

<abstract> <p>The synchronization problem of delayed nonautonomous neural networks with Caputo derivative is studied in this article. Firstly, new neural networks are proposed by introducing variable parameters into known models, and the analytical formula of the synchronous controller is given according to the new neural networks. Secondly, from the drive-response systems corresponding to the above delayed neural networks, their error system is obtained. Thirdly, by constructing the Lyapunov function and utilizing the Razumikhin-type stability theorem, the asymptotic stability of zero solution for the error system is verified, and some sufficient conditions are achieved to ensure the global asymptotic synchronization of studied neural networks. Finally, some numerical simulations are given to show the availability and feasibility of our obtained results.</p> </abstract>

Global dissipativity of non-autonomous BAM neural networks with mixed time-varying delays and discontinuous activations

Abstract In this paper, we investigate the dissipativity of a class of BAM neural networks with both time-varying and distributed delays, as well as discontinuous activations. First, the concept of the Filippov solution is extended to functional differential equations with discontinuous right-hand sides via functional differential inclusions. Then, by constructing Lyapunov functional and employing a generalized Halanay inequality, several sufficient easy-to-test conditions are successfully obtained to guarantee the global dissipativity of the Filippov solution of the considered system. The derived results extend and improve some previous publications on conventional BAM neural networks. Meanwhile, the estimations of the positive invariant and globally attractive set are given. Finally, numerical simulations are provided to demonstrate the effectiveness of our proposed results.

On the global attractivity of non-autonomous neural networks with a distributed delay

We consider a system of s nonlinear differential equations with a distributed delay and obtain global asymptotic stability conditions, which are independent of delays. The ideas of the proofs are based on the notion of a strong attractor of a vector difference equation associated with a nonlinear vector differential equation. The results are applied to Hopfield neural networks and to compartment-type models of population dynamics with Nicholson’s blowflies growth law.

Sigmoidal Approximations of a Nonautonomous Neural Network with Infinite Delay and Heaviside Function

In this paper, we approximate a nonautonomous neural network with infinite delay and a Heaviside signal function by neural networks with sigmoidal signal functions. We show that the solutions of the sigmoidal models converge to those of the Heaviside inclusion as the sigmoidal parameter vanishes. In addition, we prove the existence of pullback attractors in both cases, and the convergence of the attractors of the sigmoidal models to those of the Heaviside inclusion.

Global dissipativity and exponential synchronization of mixed time-varying delays neural networks with discontinuous activations

Abstract In this paper, the matters of dissipativity and synchronization for non-autonomous Hopfield neural networks with discontinuous activations are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. The global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and matrix measure method. Secondly, the global exponential synchronization of the addressed network drive system and the response system is realized by utilizing inequality and some analysis techniques and designing the discontinuous state feedback controller. Finally, several numerical examples are given to verify the validity of the theoretical results.

Global Exponential Stability of Hybrid Non-autonomous Neural Networks with Markovian Switching

This paper discusses the global exponential stability for a class of hybrid non-autonomous neural networks (HNNNs) with Markovian switching, which includes the factors of time delays and impulse disturbance. A novel Halanay inequality with cross terms is established by using stochastic analysis technique. Some sufficiency criteria for the global exponential stability of the HNNNs with Markovian switching are derived by the Halanay inequality and some mathematical analysis methods. The results obtained have better fault tolerance and redundancy under certain accuracy than the existing results in the literature. Finally, numerical experiments are provided to illustrate our theoretical results.

Synchronization analysis of a fractional-order non-autonomous neural network with time delay

This paper studies the problem of synchronization of a class of fractional-order non-autonomous neural network model with time delay. By using the Mittag-Leffler function and the linear feedback control, the analytic expression of synchronous controller is given. Moreover, a sufficient condition is obtained ensuring the synchronization of such delayed fractional-order neural network with Caputo derivatives by developing some new analysis methods and using the theory of delayed differential inequalities as well as constructing a suitable Lyapunov function. Finally, some numerical simulations are given to verify the effectiveness of the proposed results.

Global $$O(t^{-\alpha })$$ Synchronization of Fractional-Order Non-autonomous Neural Network Model with Time Delays Through Centralized Data-Sampling Approach

This paper aims to investigate the global $$O(t^{-\alpha })$$ synchronization of a class of fractional-order non-autonomous neural networks with time delay. Using centralized data-sampling principle and the theory of fractional differential equations, sufficient criteria for the $$O(t^{-\alpha })$$ synchronization is derived. Centralized data-sampling control is applied in the drive-response-based coupled neural networks to achieve global $$O(t^{-\alpha })$$ synchronization. It is a more effective strategy as it gives better control performance. Numerical examples are also given to illustrate the validity of the theoretical result.

Convergence on non-autonomous inertial neural networks with unbounded distributed delays

ABSTRACTIn this paper, without using reduced-order method, a class of non-autonomous inertial neural networks with time-varying connection weights and unbounded continuously distributed delays are considered. Based upon Lyapunov function method and differential inequality technique, some sufficient conditions are established to reveal that all solutions of the addressed model and their derivatives converge to zero vector, which extend and complement earlier ones in the literature. Moreover, a numerical example is provided to illustrate the correctness of the theoretical results.

Global dynamics and learning algorithm of non-autonomous neural networks with time-varying delays

In this paper, a class of non-autonomous neural networks with time-varying delays is considered. By using a new differential inequality and M-matrix, we investigate the positive invariant set and global attracting set of the networks without the assumption on boundedness of time delays or system coefficients. On this basis, we obtain sufficient conditions on the uniformly boundedness, the existence of periodic attractor and give its existence range for periodic neural networks. Furthermore, we offer a weight learning algorithms to ensure input-to-state stability, and give the state estimate and attracting set for the system. Our results can extend and improve earlier ones. Some examples and simulations are given to demonstrate the effectiveness of the obtained results.

Synchronization analysis for fractional non-autonomous neural networks by a Halanay inequality

Abstract In this paper, based on the asymptotic expansion of Mittag-Leffler function and the fractional comparison principle, an improved fractional Halanay inequality with time-varying coefficients is proved by introducing parameters λi and δ. The fractional autonomous Halanay inequality is generalized to the fractional non-autonomous case. Moreover, based on the improved fractional Halanay inequality and Lyapunov functional method, a novel sufficient condition on self synchronization of the fractional non-autonomous Hopfield neural networks with time delay is obtained. Finally, three numerical examples are given to demonstrate the effectiveness of proposed methods.

Global exponential stability of nonautonomous neural network models with unbounded delays

For a nonautonomous class of n-dimensional differential system with infinite delays, we give sufficient conditions for its global exponential stability, without showing the existence of an equilibrium point, or a periodic solution, or an almost periodic solution. We apply our main result to several concrete neural network models, studied in the literature, and a comparison of results is given. Contrary to usual in the literature about neural networks, the assumption of bounded coefficients is not required to obtain the global exponential stability. Finally, we present numerical examples to illustrate the effectiveness of our results.

Power-Rate Synchronization of Fractional-Order Nonautonomous Neural Networks with Heterogeneous Proportional Delays

This paper is concerned with the problem of global power-rate synchronization of fractional-order nonautonomous neural networks with heterogeneous proportional delays. By utilizing the Leibniz rule for fractional differentiation and an extended comparison technique, delay-dependent conditions are derived to ensure that the considered fractional-order neural network model is globally synchronous with a power decaying rate. Two examples with numerical simulations are given to demonstrate the effectiveness of the obtained results.

Invariant Set and Periodicity for Delayed Neural Networks on Time Scales

In this paper, we investigate invariant set and periodicity of non-autonomous neural networks with time-varying delays on time scales. Based calculus of time scales, we apply M-matrix and inequality analysis techniques to construct invariant set and obtain existence of a globally exponential periodic solution in the invariant set. Our results are general and can include continuous or discrete ones.