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delay-dependent and delay-independent passivity of a class of recurrent neural networks with impulse and multi-proportional delays

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Delay-dependent and delay-independent passivity of a class o...

Numerical Solution for Neutral delay Differential Equation of Constant or proportional Type using Hybrid Block Method

第四届全国神经动力学学术会议

作者：周立群 School of Mathematics Science Tianjin Normal University

The problem for passivity of a class of recurrent neural networks(RNNs) with impulse and multi-proportional delays is investigated in this paper. Several delay-dependent and delay-independent passivity criteria for the given system are obtained by establishing appropriate Lyapunov-krasovskill functionals and applying matrix inequality approach. The passivity criteria here are presented in the form of linear matrix inequalities(LMIs), which can be easily verified by Matlab Toolbox. Simultaneously, the criteria obtained here include the existing relative passivity results of RNNs without impulse or without delays as special cases and can also be extended to other RNNs with more complicated impulsive noise. Finally,a numerical example with some simulations shows that the proposed results is effective.

关键词： Recurrent neural networks proportional delay Passivity Impulse effect Lyapunov-krasovskill functional Matrix inequality

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Advances in Applied Mathematics and Mechanics 2022年第5期14卷 1138-1160页

作者： Nur Inshirah Naqiah Ismail Zanariah Abdul Majid Norazak Senu Institute for Mathematical Research Universiti Putra Malaysia43400 UPM SerdangSelangorMalaysia Department of Mathematics and Statistics Faculty of ScienceUniversiti Putra Malaysia43400 UPM SerdangSelangorMalaysia

Neutral delay Differential Equation(NDDE)is a differential problem that has regularly existed in numerous occurrences and has represented a significant role in dealing with real-life phenomena,especially on their application in biological and physiological processes.A fifth-order two-point hybrid implicit multistep block method(2PIH5)has been formulated in this research for the numerical solution of Neutral delay Differential Equation(NDDE).A Taylor series interpolation polynomial has been implemented in the formulation of the proposed *** order,consistency,and zero-stability for 2PIH5 have been *** analyses of convergence and stability test have been performed and *** initial value problems for the first-order NDDE with constant or proportional delay have been solved using the proposed block *** numerical results for the proposed method have been presented to prove the adaptability and applicability of the proposed method in solving *** proposed method is proved to be comparable with the other existing *** is assumed to be reliable and efficient for solving the first-order NDDE with constant or proportional delay.

关键词： Constant delay hybrid method multistep block method neutral delay differential equation proportional delay

Stability analysis of proportional delayed projection neural network for quadratic programming problem

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International Journal of Biomathematics 2023年第1期16卷 235-259页

作者： Xiehui Song Liqun Zhou Yu Wang Shiru Zhang Yuji Zhang School of Mathematics Science Tianjin Normal University Tianjin 300387 P.R.China

At present,projection neural network(PNN)with bounded time delay has been widely used for solving convex quadratic programming problem(QPP).However,there is little research concerning PNN with unbounded time *** this paper,we propose the proportional delayed PNN to solve QPP with equality *** utilizing homeo morphism mapping principle,we prove the proportional delayed PNN exists with unique equilibrium point which is the optimal solution of ***,delay-dependent criteria about global exponential stability(GES)and global polynomial stability(GPS)are also acquired by applying the method of variation of constants and inequality *** the other hand,when proportional delay factor q is equal to 1,the proportional delayed PNN becomes the one without time delay which still can be utilized for solving *** in most situations,q is not equal to 1,and time delay is unpredictable and may be unbounded in the actual neural network,which causes instability of ***,it is necessary to consider proportional delayed PNN.A numerical example demonstrates that,compared with the proportional delayed Lagrange neural network,the proportional delayed PNN is faster in terms of convergence *** possible reason is that appropriate parameters make the model converge to the equilibrium point along the direction of gradient descent.

关键词： Quadratic programming problem proportional delay neural networks(NNs) exponential stability polynomial stability

Polynomial dissipativity of proportional delayed BAM neural networks

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International Journal of Biomathematics 2020年第6期13卷 179-198页

作者： Lin Xing Liqun Zhou School of Mathematics Science Tianjin Normal UniversityTianjin 300387P.R.China

This paper pays close attention to the global polynomial dissipativity(GPD)for proportional delayed BAM neural networks(PDBAMNNs).The global exponential dissipativity(GED)and the global dissipativity(GD)are also talked *** the help of novel Lyapunov functionals and a generalized Halanay inequality,a set of dissipative criteria for such systems are led out,together with the global polynomial attracting set(GPAS)and the global attracting set(GAS).Further,the relationship among GPD,GED and GD is ***,a proposed theoretical condition is validated through a simulation experiment.

关键词： Global polynomial dissipativity BAM neural networks proportional delay a generalized Halanay inequality Lyapunov functionals

Global exponential stability of cellular neural networks with multi-proportional delays

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International Journal of Biomathematics 2015年第6期8卷 1-17页

作者： Liqun Zhou Yanyan Zhang School of Mathematics Science Tianjin Normal University Tianjin 300387 P. R. China

In this paper, a class of cellular neural networks （CNNs） with multi-proportional delays is studied. The nonlinear transformation yi（t） = xi（et） transforms a class of CNNs with multi-proportional delays into a class of CNNs with multi-constant delays and time- varying coefficients. By applying Brouwer fixed point theorem and constructing the delay differential inequality, several delay-independent and delay-dependent sufficient conditions are derived for ensuring the existence, uniqueness and global exponential stability of equilibrium of the system and the exponentially convergent rate is estimated. And several examples and their simulations are given to illustrate the effectiveness of obtained results.

关键词： Cellular neural networks proportional delay global exponential stability Brouwer fixed point theorem delay differential inequality.

Global Asymptotic Periodicity of Impulsive Cohen-Grossberg Neural Networks with Multi-proportional delays

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Global Asymptotic Periodicity of Impulsive Cohen-Grossberg N...