On the overlap dynamics of multi-state neural networks with a finite number of patterns

Bollé, Désiré; Dupont, Patrick; Vinck, B

doi:10.1088/0305-4470/25/10/014

Cited by 24 publications

(8 citation statements)

References 18 publications

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“…where G k ∈ R n×n (k = 0, 1) are specified in (2). Now, based on the model (3), we are in a position to introduce the delayed recurrent neural networks with Markovian jumping parameters.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Such a phenomenon is referred to as the problem of information latching [1]. A widely used approach to dealing with the information latching problem is to extract finite state representations (also called clusters, patterns, or modes) from trained networks [2], [5], [6], [7]. In other words, the RNNs may have finite modes, and the modes may switch (or jump) from one to another at different times.…”

Section: Introductionmentioning

confidence: 99%

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Exponential stability of delayed recurrent neural networks with Markovian jumping parameters

et al. 2006

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In this paper, the global exponential stability analysis problem is considered for a class of recurrent neural networks (RNNs) with time delays and Markovian jumping parameters. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. The purpose of the problem addressed is to derive some easy-to-test conditions such that the dynamics of the neural network is stochastically exponentially stable in the mean square, independent of the time delay. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish the desired sufficient conditions, and therefore the global exponential stability in the mean square for the delayed RNNs can be easily checked by utilizing the numerically efficient Matlab LMI toolbox, and no tuning of parameters is required. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exponential stability of delayed recurrent neural networks with Markovian jumping parameters

et al. 2006

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“…In practice, sometimes a neural network has finite state representations (also called modes, patterns, or clusters) and modes may switch (or jump) from one to another at different times [7][8][9][10][11][12][13]. Recently, it has been revealed in [14] that switching (or jumping) between different neural networks modes can be governed by a Markovian chain.…”

Section: Introductionmentioning

confidence: 99%

State estimation for Markovian jumping recurrent neural networks with interval time-varying delays

2009

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The paper is concerned with the state estimation problem for a class of neural networks with Markovian jumping parameters. The neural networks have a finite number of modes and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time-delays, the dynamics of the estimation error are globally stable in the mean square. A new type of Markovian jumping matrix P i is introduced in this paper. The discrete delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov-Krasovskii functional, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.

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“…In practice, sometimes a neural network has finite state representations (also called modes, patterns, or clusters), and the modes may switch (or jump) from one to another at different times [19][20][21][22][23][24][25][26]. Recently, it has been revealed in [24] that, switching (or jumping) between different neural networks modes can be governed by a Markovian chain.…”

Section: Introductionmentioning

confidence: 99%

Delay-range dependent stability criteria for neural networks with Markovian jumping parameters

Balasubramaniam

Lakshmanan

2009

Nonlinear Analysis: Hybrid Systems

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On the overlap dynamics of multi-state neural networks with a finite number of patterns

Cited by 24 publications

References 18 publications

Exponential stability of delayed recurrent neural networks with Markovian jumping parameters

Exponential stability of delayed recurrent neural networks with Markovian jumping parameters

State estimation for Markovian jumping recurrent neural networks with interval time-varying delays

Delay-range dependent stability criteria for neural networks with Markovian jumping parameters

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