On the Stability of Globally Projected Dynamical Systems

Xia, Youshen; Wang, Jun

doi:10.1023/a:1004611224835

Cited by 175 publications

(77 citation statements)

References 10 publications

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“…If function is convex and < 0, system (9) becomes a typical projection neural network model, which is widely researched in [22][23][24][25]. Similar to [24], we will give the stability analysis as follows.…”

Section: Remark 15mentioning

confidence: 99%

Neural Network to Solve Concave Games

Liu

Wang

2014

International Journal of Computer Games Technology

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Section: Remark 15mentioning

confidence: 99%

Neural Network to Solve Concave Games

Liu

Wang

2014

International Journal of Computer Games Technology

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“…Further, since the UPPAM RNNs can formalize most of the existing RNNs individuals, thus the analysis results of dynamics behaviors for UPPAM RNNs may achieve the unified conclusions for RNNs, and which can discriminate the similarity and redundant of the dynamics results among the known RNNs individuals. In particular, the achieved results here can be applied directly to many RNNs models and can improve deeply the main results of those models, for example, the Cellular Neural Networks (CNNs) [7][8][9][10][11], the Brain-State-in-Box Neural Networks (BSB NNs) [29,30], the BCOp-type RNNs [31], and other commonly used specific individuals.…”

Section: Remarkmentioning

confidence: 99%

Without Diagonal Nonlinear Requirements: The More GeneralP-Critical Dynamical Analysis for UPPAM Recurrent Neural Networks

Chen

Mao

Qiao

2013

Mathematical Problems in Engineering

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Continuous-time recurrent neural networks (RNNs) play an important part in practical applications. Recently, due to the ability of assuring the convergence of the equilibriums on the boundary line between stable and unstable, the study on the critical dynamics behaviors of RNNs has drawn especial attentions. In this paper, a new asymptotical stable theorem and two corollaries are presented for the unified RNNs, that is, the UPPAM RNNs. The analysis results given in this paper are under the generally -critical conditions, which improve substantially upon the existing relevant critical convergence and stability results, and most important, the compulsory requirement of diagonally nonlinear activation mapping in most recent researches is removed. As a result, the theory in this paper can be applied more generally.

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“…Consequently, various numerical methods which have been developed for solving dynamical systems can be used to find the approximate solution of the variational inequalities. For example, neural network techniques have been used for solving the variational inequalities, see Xia and Wang [32]. For more details on the applications of the dynamical systems, see [7-9, 11, 15, 16, 18, 20, 22, 24, 26-33].…”

Section: Introductionmentioning

confidence: 99%

Resolvent dynamical systems and mixed variational inequalities

Bin‐Mohsin¹,

Noor²,

Noor³

et al. 2017

J. Nonlinear Sci. Appl.

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In this paper, we use the dynamical systems technique to suggest and investigate some inertial proximal methods for solving mixed variational inequalities and related optimization problems. It is proved that the convergence analysis of the proposed methods requires only the monotonicity. Some special cases are also considered. Our method of proof is very simple as compared with other techniques. Ideas and techniques of this paper may be extended for other classes of variational inequalities and equilibrium problems.

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On the Stability of Globally Projected Dynamical Systems

Cited by 175 publications

References 10 publications

Neural Network to Solve Concave Games

Neural Network to Solve Concave Games

Without Diagonal Nonlinear Requirements: The More GeneralP-Critical Dynamical Analysis for UPPAM Recurrent Neural Networks

Resolvent dynamical systems and mixed variational inequalities

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