Stability analysis for delayed genetic regulatory networks with reaction--diffusion terms

Ma, Qian; Shi, Guodong; Xu, Shengyuan; Zou, Yun

doi:10.1007/s00521-011-0575-9

Cited by 32 publications

(17 citation statements)

References 37 publications

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“…Remark 2: The approach proposed in this paper can easily be applied to establish a delay-dependent and delay-ratedependent asymptotic stability criterion for GRN (1). Due to Remark 1 above, the criterion is certainly less conservative than ones in [25], [27], [28].…”

Section: Observer Designmentioning

confidence: 99%

“…To the best of authors' knowledge, the delayed GRNs with reactiondiffusion terms are only studied in [25]- [28]. Ma et al [27] introduced reaction-diffusion terms to GRNs for the first time and established delay-dependent asymptotic stability criteria. Based on the Lyapunov functional method, Zhou, Xu and Shen [26] investigated finite-time robust stochastic stability criteria for uncertain GRNs with time-varying delays and reactiondiffusion terms.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic Stability Criteria for Genetic Regulatory Networks with Time-Varying Delays and Reaction–Diffusion Terms

Han

Zhang

Wang

2015

Circuits Syst Signal Process

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This paper is concerned with the state estimation problem for genetic regulatory networks with time-varying delays and reaction-diffusion terms under Dirichlet boundary conditions. It is assumed that the nonlinear regulation function is of the Hill form. The purpose of this paper is to design a state observer to estimate the concentrations of mRNA and protein through available measurement outputs. By introducing new integral terms in a novel Lyapunov-Krasovskii functional and employing Wirtinger-based integral inequality, Wirtinger's inequality, Green's identity, convex combination approach, and reciprocally convex combination approach, an asymptotic stability criterion of the error system is established in terms of linear matrix inequalities (LMIs). The obtained stability criterion depends on the upper bounds of the delays and their derivatives. It should be highlight that if the set of LMIs are feasible, the desired observer exists and can be determined. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed designed scheme. Index Terms-Genetic regulatory networks, Reaction-diffusion terms, State estimation, Wirtinger-based integral inequality.

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Section: Observer Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Asymptotic Stability Criteria for Genetic Regulatory Networks with Time-Varying Delays and Reaction–Diffusion Terms

Han

Zhang

Wang

2015

Circuits Syst Signal Process

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“…To the best our knowledge, those works in [12][13][14][15][16][17] have researched the problem of stability analysis of delayed RDGRNs. The asymptotic stability analysis of delayed RDGRNs have been involved in [13][14][15] by constructing an appropriate LKF and applying some inequality techniques. In [16], a sufficient condition of F-T stability for delayed RDGRNs has been given by constructing an LKF including quad-slope integrations and applying the Gronwall inequality and Wirtinger-type integral inequality.…”

Section: Introductionmentioning

confidence: 99%

An r‐Order Finite‐Time State Observer for Reaction‐Diffusion Genetic Regulatory Networks with Time‐Varying Delays

Fan

Wang

et al. 2018

Complexity

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It will be settled out for the open problem of designing an r-order finite-time (F-T) state observer for reaction-diffusion genetic regulatory networks (RDGRNs) with time-varying delays. By assuming the Dirichlet boundary conditions, aiming to estimate the mRNA and protein concentrations via available network measurements. Firstly, sufficient F-T stability conditions for the filtering error system have been investigated via constructing an appropriate Lyapunov-Krasovskii functional (LKF) and using several integral inequalities and (reciprocally) convex technique simultaneously. These conditions are delay-dependent and reaction-diffusion-dependent and can be checked by MATLAB toolbox. Furthermore, a method is proposed to design an r -order F-T state observer, and the explicit expressions of observer gains are given. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.

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“…In particular, we may mention 2D Monte Carlo simulations with mRNA and protein diffusion [21], 3D Monte Carlo simulations with mRNA diffusion [22,23], mean-field analysis focused on the non-coding RNA diffusion [24], and general mean-field analysis of the stability of solutions of reaction-diffusion equations [25].…”

Section: Introductionmentioning

confidence: 99%

“…Despite their simplicity, the results presented are novel (compared to those obtained in Refs. [21][22][23][24][25]) and instructive.…”

Section: Introductionmentioning

confidence: 99%

A generic 3D kinetic model of gene expression

Zhdanov¹

2012

Open Physics

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Abstract:Recent experiments show that mRNAs and proteins can be localized both in prokaryotic and eukaryotic cells. To describe such situations, I present a 3D mean-field kinetic model aimed primarily at gene expression in prokaryotic cells, including the formation of mRNA, its translation into protein, and slow diffusion of these species. Under steady-state conditions, the mRNA and protein spatial distribution is described by simple exponential functions. The protein concentration near the gene transcribed into mRNA is shown to depend on the protein and mRNA diffusion coefficients and degradation rate constants.

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Stability analysis for delayed genetic regulatory networks with reaction--diffusion terms

Cited by 32 publications

References 37 publications

Asymptotic Stability Criteria for Genetic Regulatory Networks with Time-Varying Delays and Reaction–Diffusion Terms

Asymptotic Stability Criteria for Genetic Regulatory Networks with Time-Varying Delays and Reaction–Diffusion Terms

An r‐Order Finite‐Time State Observer for Reaction‐Diffusion Genetic Regulatory Networks with Time‐Varying Delays

A generic 3D kinetic model of gene expression

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