Stability of genetic regulatory networks with time-varying delay: Delta operator method

Zhou, Qi; Shao, Xueying; Karimi, Hamid Reza; Zhu, Jin

doi:10.1016/j.neucom.2014.08.025

Cited by 21 publications

(4 citation statements)

References 32 publications

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“…The results showed that, under different biological parameters, coupling delay would induce the system to generate dynamic behavior of stable or stable and unstable phase switch [17]. Zhou et al discussed the stability of indeterministic systems with variable delays, which took into account both biochemical parameter uncertainty and generalized activation effect [18]. Wang et al obtained the bifurcation characteristics by studying the positive equilibrium point of the two-gene four-delay gene regulatory network model [19].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis and Fractional PD Control of Gene Regulatory Networks with sRNA

et al. 2023

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This paper investigates the problem of bifurcation analysis and bifurcation control of a fractional-order gene regulatory network with sRNA. Firstly, the process of stability change of system equilibrium under the influence of the sum of time delay is discussed, the critical condition of Hopf bifurcation is explored, and the effect of fractional order on the system stability domain. Secondly, aiming at the system’s instability caused by a large time delay, we design a controller to improve the system’s stability and derive the parameter conditions that satisfy the system’s stability. It is found that changing the parameter values of the controller within a certain range can control the system’s nonlinear behaviours and effectively expand the stability range. Then, a numerical example is given to illustrate the results of this paper.

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Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis and Fractional PD Control of Gene Regulatory Networks with sRNA

et al. 2023

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“…After that, a lot of research results have been shown for delta operator systems. Using a delta operator approach, a fuzzy fault detection filter and a stability problem have been investigated for uncertain fuzzy and networked control systems, respectively [15,16]. Saturation is a common problem in modern engineering field.…”

Section: Introductionmentioning

confidence: 99%

Stabilization for two-dimensional delta operator systems with time-varying delays and actuator saturation

2018

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In this paper, stabilization is studied for a two-dimensional delta operator system with time-varying delays and actuator saturation. Both lower and upper bounds of the time-varying delays are considered. An estimate of the domain of attraction for the two-dimensional delta operator system is introduced to analyze stability of the closed-loop system. A state feedback controller is designed via a Lyapunov-Krasovskii functional approach for the two-dimensional delta operator system with time-varying delays and actuator saturation. Two numerical examples are given to illustrate the effectiveness and advantages of the developed techniques.

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“…For this, a lot of GRNs models have been built to track the concentration of mRNA and protein, like Boolean model [ 3 , 4 ], Bayesian model [ 5 – 7 ], differential equation model [ 8 – 11 ], and state-space model [ 12 , 13 ]. However, due to the uncertainties of the system, time-varying delays [ 14 – 16 ] and data missing [ 17 , 18 ] in real gene expression process, the measurements obtained from the sensor are usually contaminated by noise and cannot represent the true values well. Thus, a lot of filtering methods are proposed to reveal the true values.…”

Section: Introductionmentioning

confidence: 99%

Kalman Filtering for Genetic Regulatory Networks with Missing Values

Lin

Liu

Lai

et al. 2017

Computational and Mathematical Methods in Medicine

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The filter problem with missing value for genetic regulation networks (GRNs) is addressed, in which the noises exist in both the state dynamics and measurement equations; furthermore, the correlation between process noise and measurement noise is also taken into consideration. In order to deal with the filter problem, a class of discrete-time GRNs with missing value, noise correlation, and time delays is established. Then a new observation model is proposed to decrease the adverse effect caused by the missing value and to decouple the correlation between process noise and measurement noise in theory. Finally, a Kalman filtering is used to estimate the states of GRNs. Meanwhile, a typical example is provided to verify the effectiveness of the proposed method, and it turns out to be the case that the concentrations of mRNA and protein could be estimated accurately.

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Stability of genetic regulatory networks with time-varying delay: Delta operator method

Cited by 21 publications

References 32 publications

Bifurcation Analysis and Fractional PD Control of Gene Regulatory Networks with sRNA

Bifurcation Analysis and Fractional PD Control of Gene Regulatory Networks with sRNA

Stabilization for two-dimensional delta operator systems with time-varying delays and actuator saturation

Kalman Filtering for Genetic Regulatory Networks with Missing Values

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