Exponential stability of stochastic high-order BAM neural networks with time delays and impulsive effects

In this paper, we consider the problem on exponential stability analysis of the stochastic impulsive high-order BAM neural networks with time delays. Through employing Lyapunov function method and stochastic bidirected halanay inequality, we constitute exponential stability of the stochastic impulsive high-order BAM neural networks with its estimated exponential convergence rate and feasible interval of impulsive strength. An example illustrates the main results.     

Impulsive effects on stability of high-order BAM neural networks with time delays

The problem of Impulsive effects on stability analysis of high-order BAM neural networks with time delays is investigated in this paper. By using the Lyapunov technique and Razumikhin method, we characterize theoretically the aggregated effects of impulse and stability properties of impulse-free version and then analyze the stabilizing mechanism and destabilizing mechanism of impulses, respectively. The present approaches allow us to estimate the feasible upper bounds of impulse strengths and can also extend to the more general impulsive nonlinear systems with delays. To demonstrate the effectiveness of theoretical results, several numerical examples are given.     

Stochastic stability of impulsive BAM neural networks with time delays

The problem of stability analysis of stochastic BAM neural networks with time delays and impulse effects is investigated in this paper. Using the Lyapunov technique and the generalized Hanalay inequality, we characterize theoretically the aggregated effects of impulse and stability properties of the impulse-free version. The present approaches allow us to estimate the feasible upper bounds of impulse strengths and can also extend to the more general impulsive nonlinear systems with delays.     

Impulsive effect on global exponential stability of BAM fuzzy cellular neural networks with time-varying delays

In this article, a class of impulsive bidirectional associative memory (BAM) fuzzy cellular neural networks (FCNNs) with time-varying delays is formulated and investigated. By employing delay differential inequality and M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM FCNNs with time-varying delays are obtained. In particular, a precise estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive perturbation intention. It is believed that these results are significant and useful for the design and applications of BAM FCNNs. An example is given to show the effectiveness of the results obtained here.     

Asymptotic stability of impulsive high-order Hopfield type neural networks

In this paper, we discuss impulsive high-order Hopfield type neural networks. Investigating their global asymptotic stability, by using Lyapunov function method, sufficient conditions that guarantee global asymptotic stability of networks are given. These criteria can be used to analyse the dynamics of biological neural systems or to design globally stable artificial neural networks. Two numerical examples are given to illustrate the effectiveness of the proposed method.     

Global exponential stability of impulsive high-order Hopfield type neural networks with delays

In this paper, we investigate the global exponential stability of impulsive high-order Hopfield type neural networks with delays. By establishing the impulsive delay differential inequalities and using the Lyapunov method, two sufficient conditions that guarantee global exponential stability of these networks are given, and the exponential convergence rate is also obtained. A numerical example is given to demonstrate the validity of the results.     

On the exponential synchronization of stochastic impulsive chaotic delayed neural networks

In this paper, the exponential synchronization of stochastic impulsive chaotic delayed neural networks is investigated. Based on the Lyapunov function method, time-varying delay feedback control technique and the efficient modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical chaotic delayed neural networks with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities (LMIs), which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. Comparing with the existing works that consider single perturbation (stochastic or impulsive one), the proposed method can provide a more general framework for the synchronization of multi-perturbation chaotic systems, which is favorable for practical application in secure communication. Finally, numerical simulations verify the effectiveness of the proposed method.     

Exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays

This paper considers the problems of global exponential stability and exponential convergence rate for impulsive high-order Hopfield-type neural networks with time-varying delays. By using the method of Lyapunov functions, some sufficient conditions for ensuring global exponential stability of these networks are derived, and the estimated exponential convergence rate is also obtained. As an illustration, an numerical example is worked out using the results obtained.     

Global Exponential Stability of High-Order Bidirectional Associative Memory (BAM) Neural Networks with Proportional Delays

Neural Processing Letters - This paper considers the global exponential stability (GES) of high-order bidirectional associative memory (BAM) neural networks with proportional delays. Here,...     

Global asymptotic stability of impulsive fractional-order BAM neural networks with time delay

Neural Computing and Applications - In this paper, we study the global asymptotic stability of fractional-order BAM neural networks. We take both time delay and impulsive effects into...     

Mean square exponential stability of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays

In this paper, we establish a method to study the mean square exponential stability of the zero solution of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays. By using the properties of M-cone and inequality technique, we obtain some sufficient conditions ensuring mean square exponential stability of the zero solution of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays. The sufficient conditions are easily checked in practice by simple algebra methods and have a wider adaptive range. Two examples are also discussed to illustrate the efficiency of the obtained results.     

Global Asymptotic Periodic Synchronization for Delayed Complex-Valued BAM Neural Networks via Vector-Valued Inequality Techniques

In this paper, we are concerned with a class of delayed complex-valued BAM neural networks. In stead of using the priori estimate method of periodic solutions, by means of combining Mawhin’s continuation theorem of coincidence degree theory with novel LMI method and some analysis techniques, a novel LMI-based sufficient condition is obtained for the existence of periodic solutions of the delayed complex-valued BAM neural networks. Then by using novel LMI method, a novel sufficient condition on global asymptotic periodic synchronization of above complex-valued BAM neural networks is established.     

Exponential p-stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays

In this paper, we study the impulsive stochastic Cohen–Grossberg neural networks with mixed delays. By establishing an L-operator differential inequality with mixed delays and using the properties of M-cone and stochastic analysis technique, we obtain some sufficient conditions ensuring the exponential p-stability of the impulsive stochastic Cohen–Grossberg neural networks with mixed delays. These results generalize a few previous known results and remove some restrictions on the neural networks. Two examples are also discussed to illustrate the efficiency of the obtained results.     

Global Robust Exponential Stability of Uncertain Neutral High-Order Stochastic Hopfield Neural Networks with Time-Varying Delays

In this paper, a class of uncertain neutral high-order stochastic Hopfield neural networks with time-varying delays is investigated. By using Lyapunov-Krasovskii functional and stochastic analysis approaches, new and less conservative delay-dependent stability criteria is presented in terms of linear matrix inequalities to guarantee the neural networks to be globally robustly exponentially stable in the mean square for all admissible parameter uncertainties and stochastic perturbations. Numerical simulations are carried out to illustrate the main results.     

Global asymptotic stability of uncertain stochastic bi-directional associative memory networks with discrete and distributed delays

In this paper, the global asymptotic stability analysis problem is investigated for a class of stochastic bi-directional associative memory (BAM) networks with mixed time-delays and parameter uncertainties. The mixed time-delays consist of both the discrete and the distributed delays, the uncertainties are assumed to be norm-bounded, and the neural network are subject to stochastic disturbances described by a Brownian motion. Without assuming the monotonicity and differentiability of activation functions, we employ the Lyapunov–Krasovskii stability theory and some new developed techniques to establish sufficient conditions for the stochastic delayed BAM networks to be globally asymptotically stable in the mean square. These conditions are expressed in terms of the feasibility to a set of linear matrix inequalities (LMIs) that can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A simple example is exploited to show the usefulness of the derived LMI-based stability conditions.     

Impulsive stabilization of high-order hopfield-type neural networks with time-varying delays

This paper studies the problems of global exponential stability for impulsive high-order Hopfield-type neural networks (NNs) with time-varying delays. By employing the Lyapunov-Razumikhin technique, some criteria ensuring global exponential stability are derived. Our results are then used to obtain some sufficient conditions under which some NNs can be forced to converge by impulsive control. Numerical examples are also discussed to illustrate our results.     

Stability of uncertain impulsive stochastic fuzzy neural networks with two additive time delays in the leakage term

This paper is concerned with the stability problem for a class of impulsive neural networks model, which includes simultaneously parameter uncertainties, stochastic disturbances and two additive time-varying delays in the leakage term. By constructing a suitable Lyapunov–Krasovskii functional that uses the information on the lower and upper bound of the delay sufficiently, a delay-dependent stability criterion is derived by using the free-weighting matrices method for such Takagi–Sugeno fuzzy uncertain impulsive stochastic recurrent neural networks. The obtained conditions are expressed with linear matrix inequalities (LMIs) whose feasibility can be checked easily by MATLAB LMI Control toolbox. Finally, the theoretical result is validated by simulations.     

Decentralized Event-triggered Stability Analysis of Neutral-type BAM Neural Networks with Markovian Jump Parameters and Mixed Time Varying Delays

This paper investigates decentralized event-triggered stability analysis of neutral-type BAM neural networks with Markovian jump parameters and mixed time varying delays. We apply the decentralized event triggered approach to the bidirectional associative memory (BAM) neural networks to reduce the network traffic and the resource of computation. A bidirectional associative memory neural networks is constructed with the mixed time varying delays and Markov process parameters. The criteria for the asymptotically stability are proposed by using with the Lyapunov-Krasovskii functional method, reciprocal convex property and Jensen’s inequality. Stability condition of neutral-type BAM neural networks with Markovian jump parameters and mixed delays is established in terms of linear matrix inequalities. Finally three numerical examples are given to demonstrate the effectiveness of the proposed results     

Global asymptotic stability of delay BAM neural networks with impulses via nonsmooth analysis

In this paper, we study global asymptotic stability of delay bi-directional associative memory (BAM) neural networks with impulses. We obtain a sufficient condition of ensuring existence and uniqueness of equilibrium point for delay BAM neural networks with impulses basing on nonsmooth analysis. And we give a criteria of global asymptotic stability of the unique equilibrium point for delay BAM neural networks with impulses using Lyapunov method. At last, we present examples to illustrate that our results are feasible.     

Global Exponential Stability for Impulsive BAM Neural Networks with Distributed Delays on Time Scales

In this paper, by utilizing the time scale calculus theory, topological degree theory and Hölder’s inequality on time scales, we analyze a class of impulsive BAM neural networks with distributed delays on time scales. Some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the equilibrium point. Finally, an example is provided to demonstrate the effectiveness of the results.