scholarly journals Bifurcation Analysis and Impulsive Control of Genetic Regulatory Networks with Multi Delays

2019 ◽  
Vol 23 (4) ◽  
pp. 743-748 ◽  
Author(s):  
Feng Liu ◽  
Jie Ren ◽  
Ting Dong ◽  
Shiqi Zheng ◽  
◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Regulatory Network ◽  
Regulatory Networks ◽  
Control Method ◽  
Impulsive Control ◽  
Genetic Regulatory Networks ◽  
Genetic Regulatory Network ◽  
The Stability ◽  
Theoretical Results

In this study, the stability and Hopf bifurcation of a genetic regulatory network with delays are addressed. Some bifurcations may cause network oscillation and induce instability. An impulsive control method is proposed to control the bifurcations. A numerical simulation was performed to demonstrate the effectiveness of the theoretical results.

scholarly journals Effect of Leakage Delay on Stability of Neutral-Type Genetic Regulatory Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Li Li ◽  
Yongqing Yang ◽  
Chuanzhi Bai
Keyword(s):  
Regulatory Network ◽  
Regulatory Networks ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Genetic Regulatory Networks ◽  
Genetic Regulatory Network ◽  
Leakage Delay ◽  
Leakage Delays ◽  
The Stability

The stability of neutral-type genetic regulatory networks with leakage delays is considered. Firstly, we describe the model of genetic regulatory network with neutral delays and leakage delays. Then some sufficient conditions are derived to ensure the asymptotic stability of the genetic regulatory network by the Lyapunov functional method. Further, the effect of leakage delay on stability is discussed. Finally, a numerical example is given to show the effectiveness of the results.

scholarly journals Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Fu-Dong Li ◽  
Qi Zhu ◽  
Hao-Tian Xu ◽  
Lin Jiang
Keyword(s):  
Stability Analysis ◽  
Integral Inequality ◽  
Regulatory Network ◽  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Genetic Regulatory Network ◽  
Double Integral ◽  
Integral Term ◽  
Double Inequality ◽  
The Stability

Time delay arising in a genetic regulatory network may cause the instability. This paper is concerned with the stability analysis of genetic regulatory networks with interval time-varying delays. Firstly, a relaxed double integral inequality, named as Wirtinger-type double integral inequality (WTDII), is established to estimate the double integral term appearing in the derivative of Lyapunov-Krasovskii functional with a triple integral term. And it is proved theoretically that the proposed WTDII is tighter than the widely used Jensen-based double inequality and the recently developed Wiringter-based double inequality. Then, by applying the WTDII to the stability analysis of a delayed genetic regulatory network, together with the usage of useful information of regulatory functions, several delay-range- and delay-rate-dependent (or delay-rate-independent) criteria are derived in terms of linear matrix inequalities. Finally, an example is carried out to verify the effectiveness of the proposed method and also to show the advantages of the established stability criteria through the comparison with some literature.

scholarly journals State Observer Design for Delayed Genetic Regulatory Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Li-Ping Tian ◽  
Zhi-Jun Wang ◽  
Amin Mohammadbagheri ◽  
Fang-Xiang Wu
Keyword(s):  
Regulatory Network ◽  
Regulatory Networks ◽  
Estimation Error ◽  
State Observer ◽  
Genetic Regulatory Networks ◽  
Genetic Regulatory Network ◽  
Observer Design ◽  
Linear Matrix ◽  
Globally Asymptotically Stable ◽  
Internal States

Genetic regulatory networks are dynamic systems which describe the interactions among gene products (mRNAs and proteins). The internal states of a genetic regulatory network consist of the concentrations of mRNA and proteins involved in it, which are very helpful in understanding its dynamic behaviors. However, because of some limitations such as experiment techniques, not all internal states of genetic regulatory network can be effectively measured. Therefore it becomes an important issue to estimate the unmeasured states via the available measurements. In this study, we design a state observer to estimate the states of genetic regulatory networks with time delays from available measurements. Furthermore, based on linear matrix inequality (LMI) approach, a criterion is established to guarantee that the dynamic of estimation error is globally asymptotically stable. A gene repressillatory network is employed to illustrate the effectiveness of our design approach.

Numerical Methods for Genetic Regulatory Network Identification Based on a Variational Approach

2016 ◽  
Vol 16 (1) ◽  
pp. 77-103
Author(s):  
Xiaobing Feng ◽  
Miun Yoon
Keyword(s):  
Differential Equation ◽  
Variational Principle ◽  
Numerical Methods ◽  
Regulatory Network ◽  
Regulatory Networks ◽  
Numerical Solutions ◽  
Genetic Regulatory Networks ◽  
Genetic Regulatory Network ◽  
Variational Framework ◽  
Network Identification

AbstractThis paper studies differential equation-based mathematical models and their numerical solutions for genetic regulatory network identification. The primary objectives are to design, analyze, and test a general variational framework and numerical methods for seeking its approximate solutions for reverse engineering genetic regulatory networks from microarray datasets. In the proposed variational framework, no structure assumption on the genetic network is presumed, instead, the network is solely determined by the microarray profile of the network components and is identified through a well chosen variational principle which minimizes an energy functional. The variational principle serves not only as a selection criterion to pick up the right solution of the underlying differential equation model but also provides an effective mathematical characterization of the small-world property of genetic regulatory networks which has been observed in lab experiments. Five specific models within the variational framework and efficient numerical methods and algorithms for computing their solutions are proposed and analyzed. Model validations using both synthetic network datasets and subnetwork datasets of Saccharomyces cerevisiae (yeast) and E. coli are performed on all five proposed variational models and a performance comparison versus some existing genetic regulatory network identification methods is also provided.

Problems for Structure Learning

2010 ◽  
pp. 310-333 ◽  
Author(s):  
Frank Wimberly ◽  
David Danks ◽  
Clark Glymour ◽  
Tianjiao Chu
Keyword(s):  
Graphical Models ◽  
Microarray Data ◽  
Regulatory Network ◽  
Conditional Independence ◽  
Regulatory Networks ◽  
Structure Learning ◽  
Genetic Regulatory Networks ◽  
Genetic Regulatory Network ◽  
Complexity Of Algorithms ◽  
Realistic Data

Machine learning methods to find graphical models of genetic regulatory networks from cDNA microarray data have become increasingly popular in recent years. We provide three reasons to question the reliability of such methods: (1) a major theoretical challenge to any method using conditional independence relations; (2) a simulation study using realistic data that confirms the importance of the theoretical challenge; and (3) an analysis of the computational complexity of algorithms that avoid this theoretical challenge. We have no proof that one cannot possibly learn the structure of a genetic regulatory network from microarray data alone, nor do we think that such a proof is likely. However, the combination of (i) fundamental challenges from theory, (ii) practical evidence that those challenges arise in realistic data, and (iii) the difficulty of avoiding those challenges leads us to conclude that it is unlikely that current microarray technology will ever be successfully applied to this structure learning problem.

scholarly journals Analysis of the Stability and Hopf Bifurcation of Currency Supply Delay in an Opened Kaldorian Business Cycle Model

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Liming Zhao ◽  
Zhipei Zhao
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Business Cycle ◽  
Three Dimension ◽  
Cycle Model ◽  
Macroeconomic Policies ◽  
Existence Of Equilibrium ◽  
Business Cycle Model ◽  
The Stability ◽  
Theoretical Results

First of all, we establish a three-dimension open Kaldorian business cycle model under the condition of the fixed exchange rate. Secondly, with regard to the model, we discuss the existence of equilibrium point and the stability of the system near it with a time delay in currency supply as the bifurcating parameters of the system. Thirdly, we discuss the existence of Hopf bifurcation and investigate the stability of periodic solution generated by the Hopf bifurcation; then the direction of the Hopf bifurcation is given. Finally, a numerical simulation is given to confirm the theoretical results. This paper plays an important role in theoretical researching on the model of business cycle, and it is crucial for decision-maker to formulate the macroeconomic policies with the conclusions of this paper.

EXISTENCE OF LIMIT CYCLES IN THE REPRESSILATOR EQUATIONS

2009 ◽  
Vol 19 (12) ◽  
pp. 4097-4106 ◽  
Author(s):  
OLGUŢA BUŞE ◽  
ALEXEY KUZNETSOV ◽  
RODRIGO A. PÉREZ
Keyword(s):  
Protein Synthesis ◽  
Hopf Bifurcation ◽  
Circadian Clock ◽  
Limit Cycles ◽  
Regulatory Network ◽  
Regulatory Networks ◽  
Large Range ◽  
Oscillatory Behavior ◽  
Genetic Regulatory Network ◽  
Maximal Rate

The Repressilator is a genetic regulatory network used to model oscillatory behavior of more complex regulatory networks like the circadian clock. We prove that the Repressilator equations undergo a supercritical Hopf bifurcation as the maximal rate of protein synthesis increases, and find a large range of parameters for which there is a cycle.

Genetic Regulatory Network Analysis for Rpe65 in the Eye of BXD Mice

2011 ◽  
Vol 282-283 ◽  
pp. 248-252
Author(s):  
Hong Lu ◽  
Huai Jin Guan ◽  
Hui Chen ◽  
Lu Lu
Keyword(s):  
Network Analysis ◽  
Regulatory Network ◽  
Regulatory Networks ◽  
Likelihood Ratio Statistic ◽  
Critical Role ◽  
Genetic Regulatory Networks ◽  
Genetic Regulatory Network ◽  
Microarray Probe ◽  
Inherited Retinal Dystrophies ◽  
Retinal Dystrophies

Previous studies have revealed that the mutation of Rpe65plays a critical role in inherited retinal dystrophies. However, little is known about the genetic regulatory network for Rpe65 and inherited retinal dystrophies. We combined gene expression microarray analysis and quantitative trait loci (QTL) mapping to characterize the genetic regulatory network for Rpe65 expression in the eye of BXD recombinant inbred (RI) mice. Our analysis found that the expression level of Rpe65exhibited much variation in the eye across the BXD RI strains and between the parental strains, C57BL/6J and DBA/2J. Expression QTL (eQTL) mapping showed that one microarray probe set of Rpe65 has highly significant linkage (Likelihood Ratio Statistic) scores. Moreover, the QTL was mapped to within 3 Mb of the location of the gene itself (Rpe65) as a cis-acting QTL. Through mapping the joint modulation of Rpe65, we identified Ches1/Foxn3 as downstream gene of Rpe65. Then the gene co-regulatory network analysis was constructed. The genetic genomics approach demonstrates the importance and the potential power of the eQTL studies in identifying genetic regulatory networks that contribute to inherited retinal dystrophies.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

scholarly journals Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Hongwei Luo ◽  
Jiangang Zhang ◽  
Wenju Du ◽  
Jiarong Lu ◽  
Xinlei An
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Points ◽  
Bifurcation Theorem ◽  
Center Manifold Theorem ◽  
Governing System ◽  
Normal Form Method ◽  
The Stability ◽  
System Frequency ◽  
Realistic Significance ◽  
Theoretical Results

A PI hydroturbine governing system with saturation and double delays is generated in small perturbation. The nonlinear dynamic behavior of the system is investigated. More precisely, at first, we analyze the stability and Hopf bifurcation of the PI hydroturbine governing system with double delays under the four different cases. Corresponding stability theorem and Hopf bifurcation theorem of the system are obtained at equilibrium points. And then the stability of periodic solution and the direction of the Hopf bifurcation are illustrated by using the normal form method and center manifold theorem. We find out that the stability and direction of the Hopf bifurcation are determined by three parameters. The results have great realistic significance to guarantee the power system frequency stability and improve the stability of the hydropower system. At last, some numerical examples are given to verify the correctness of the theoretical results.

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