Stability analysis for stochastic BAM neural networks with Markovian jumping parameters

Wang, Guanjun; Cao, Jinde; Xu, Ming

doi:10.1016/j.neucom.2009.05.001

Cited by 25 publications

(6 citation statements)

References 19 publications

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“…Remark In the work of Wang et al, stability issues for stochastic BAM neural networks with Markovian jumping parameters are analyzed. Sakthivel et al delivered the concept of BAM neural networks in the way of exponentially stable and in the work of Cao and Song, Cohen‐Grossberg BAM neural networks with time‐varying delays are considered.…”

Section: Uncertain Discrete‐time Neural Networkmentioning

confidence: 99%

“…Furthermore, systems with Markovian jumping parameters are useful in modeling abrupt phenomena such as random failures, changes in the Markovian jumping parameters are usually dominated by discrete‐state homogenous Markov process, and each state of the parameters represents a mode of the system. Recently, the stability of stochastic neural networks with Markovian switching has received much attention …”

Section: Introductionmentioning

confidence: 99%

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Global exponential stability of antiperiodic solutions for impulsive discrete‐time Markovian jumping stochastic BAM neural networks with additive time‐varying delays and leakage delay

Sowmiya

Raja

Cao

et al. 2018

Adaptive Control & Signal

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This paper presents a global exponential stability of antiperiodic solution for a class of impulsive discrete-time Markovian jumping stochastic bidirectional associative memory neural networks with additive time-varying delays and leakage delay. By utilizing the Lyapunov-Krasovskii functional and contraction mapping principle, several sufficient conditions and linear matrix inequalities are derived for verifying globally exponentially stable in the mean square. There is a new delay-dependent criterion for checking the existence, uniqueness, and global stability for antiperiodic solution. Meantime, by using the numerically efficient MATLAB Toolbox, simulation examples are offered to show the effectiveness and usefulness of the obtained result.

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Section: Uncertain Discrete‐time Neural Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global exponential stability of antiperiodic solutions for impulsive discrete‐time Markovian jumping stochastic BAM neural networks with additive time‐varying delays and leakage delay

Sowmiya

Raja

Cao

et al. 2018

Adaptive Control & Signal

Self Cite

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“…The BAM NN model is a two-layer, nonlinear feedback network model, and it has formulated that the neurons in one layer are always interconnected to neurons in another layer, which has been widely used because of their mathematical modeling capabilities. As a result, BAM NN models have received significant research attention in both areas of the field of both mathematical and practical analysis [8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks

et al. 2020

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We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper. Whether the real and imaginary parts of quaternion-valued activation functions are expressed implicitly or explicitly, they are considered to meet the global Lipschitz condition in the quaternion field. New sufficient conditions are derived by applying the principle of homeomorphism, Lyapunov fractional-order method and linear matrix inequality (LMI) approach for the two cases of activation functions. The results confirm the existence, uniqueness and global asymptotic stability of the system’s equilibrium point. Finally, two numerical examples with their simulation results are provided to show the effectiveness of the obtained results.

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“…So, the stochastic disturbance is probably the main resource of the performance degradation in the implemented neural networks. Therefore, the stability of stochastic neural networks with delay has attracted increasing interests and some results related to stochastic disturbances have been published . Recently, a class of neural networks with Markovian jump parameters has received a great deal of research attention because this class of neural networks has been recognized to be the best system to model the phenomenon of information latching and the abrupt phenomena such as random failures or repairs of the components, sudden environmental changes, changing subsystem interconnections, and so forth.…”

Section: Introductionmentioning

confidence: 99%

Exponential stability for markovian jumping stochastic BAM neural networks with mode‐dependent probabilistic time‐varying delays and impulse control

et al. 2014

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In this article, an exponential stability analysis of Markovian jumping stochastic bidirectional associative memory (BAM) neural networks with mode‐dependent probabilistic time‐varying delays and impulsive control is investigated. By establishment of a stochastic variable with Bernoulli distribution, the information of probabilistic time‐varying delay is considered and transformed into one with deterministic time‐varying delay and stochastic parameters. By fully taking the inherent characteristic of such kind of stochastic BAM neural networks into account, a novel Lyapunov‐Krasovskii functional is constructed with as many as possible positive definite matrices which depends on the system mode and a triple‐integral term is introduced for deriving the delay‐dependent stability conditions. Furthermore, mode‐dependent mean square exponential stability criteria are derived by constructing a new Lyapunov‐Krasovskii functional with modes in the integral terms and using some stochastic analysis techniques. The criteria are formulated in terms of a set of linear matrix inequalities, which can be checked efficiently by use of some standard numerical packages. Finally, numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 20: 39–65, 2015

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Stability analysis for stochastic BAM neural networks with Markovian jumping parameters

Cited by 25 publications

References 19 publications

Global exponential stability of antiperiodic solutions for impulsive discrete‐time Markovian jumping stochastic BAM neural networks with additive time‐varying delays and leakage delay

Global exponential stability of antiperiodic solutions for impulsive discrete‐time Markovian jumping stochastic BAM neural networks with additive time‐varying delays and leakage delay

Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks

Exponential stability for markovian jumping stochastic BAM neural networks with mode‐dependent probabilistic time‐varying delays and impulse control

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