Stochastic BAM Neural Networks Research Articles

Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays.

This paper discusses the issue of stability analysis for a class of impulsive stochastic bidirectional associative memory neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are modeled as a continuous-time discrete-state Markov chain. Based on a novel Lyapunov-Krasovskii functional, the generalized Itô's formula, mathematical induction, and stochastic analysis theory, a linear matrix inequality approach is developed to derive some novel sufficient conditions that guarantee the exponential stability in the mean square of the equilibrium point. At the same time, we also investigate the robustly exponential stability in the mean square of the corresponding system with unknown parameters. It should be mentioned that our stability results are delay-dependent, which depend on not only the upper bounds of time delays but also their lower bounds. Moreover, the derivatives of time delays are not necessarily zero or smaller than one since several free matrices are introduced in our results. Consequently, the results obtained in this paper are not only less conservative but also generalize and improve many earlier results. Finally, two numerical examples and their simulations are provided to show the effectiveness of the theoretical results.

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.

Exponential stability for stochastic BAM networks with discrete and distributed delays

In this paper, we investigate exponential stability for stochastic BAM networks with mixed delays. The mixed delays include discrete and distributed time-delays. The purpose of this paper is to establish some criteria to ensure the delayed stochastic BAM neural networks are exponential stable in the mean square. A sufficient condition is established by consructing suitable Lyapunov functionals. The condition is expressed in terms of the feasibility to a couple LMIs. Therefore, the exponential stability of the stochastic BAM networks with discrete and distributed delays can be easily checked by using the numerically efficient Matlab LMI toobox. A simple example is given to demonstrate the usefulness of the derived LMI-based stability conditions.

New robust passivity criteria for stochastic fuzzy BAM neural networks with time-varying delays

In this paper, we consider the problem of passivity analysis issue for a class of stochastic fuzzy BAM neural networks with time varying delays. By employing the idea of delay-fractioning technique and Lyapunov stability theory, a new set of sufficient conditions are derived in terms of linear matrix inequalities for obtaining the passivity condition of the considered neural network model. First, we derive the passivity condition for stochastic fuzzy BAM neural networks with time varying delays and then the result is extended to the case with uncertainties. Two numerical examples are given to illustrate the effectiveness and conservatism of the obtained results.

Exponential Stability for Discrete-Time Stochastic BAM Neural Networks with Discrete and Distributed Delays

This paper deals with the stability analysis problem for a class of discrete-time stochastic BAM neural networks with discrete and distributed time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional and employing M-matrix theory, we find some sufficient conditions ensuring the global exponential stability of the equilibrium point for stochastic BAM neural networks with time-varying delays. The conditions obtained here are expressed in terms of LMIs whose feasibility can be easily checked by MATLAB LMI Control toolbox. A numerical example is presented to show the effectiveness of the derived LMI-based stability conditions.

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.

Mean square exponential stability in high-order stochastic impulsive BAM neural networks with time-varying delays

In this paper, a class of stochastic impulsive high-order BAM neural networks with time-varying delays is considered. By using Lyapunov functional method, LMI method and mathematics induction, some sufficient conditions are derived for the globally exponential stability of the equilibrium point of the neural networks in mean square. It is believed that these results are significant and useful for the design and applications of impulsive stochastic high-order BAM neural networks.

New exponential stability criteria for stochastic BAM neural networks with impulses

In this paper, we study the global exponential stability of time-delayed stochastic bidirectional associative memory neural networks with impulses and Markovian jumping parameters. A generalized activation function is considered, and traditional assumptions on the boundedness, monotony and differentiability of activation functions are removed. We obtain a new set of sufficient conditions in terms of linear matrix inequalities, which ensures the global exponential stability of the unique equilibrium point for stochastic BAM neural networks with impulses. The Lyapunov function method with the Itô differential rule is employed for achieving the required result. Moreover, a numerical example is provided to show that the proposed result improves the allowable upper bound of delays over some existing results in the literature.