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Author:
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Category :
Languages : en
Pages : 18
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
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Author:
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Category :
Languages : en
Pages : 20
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Author: Jiewei Li
Publisher:
ISBN: 9781361000014
Category :
Languages : en
Pages :
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This dissertation, "Stability Analysis of Uncertain Genetic Regulatory Newtworks" by Jiewei, Li, 李劼伟, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Genetic regulatory network (GRN) is a fundamental research area in systems biology. This thesis studies the stability of a class of GRN models. First, a condition is proposed to ensure the robust stability of uncertain GRNs with SUM regulatory functions. It is assumed that the uncertainties are in the form of a parameter vector that determines the coefficients of the model via given functions. Then, the global asymptotic stability conditions of uncertain GRNs affected by disturbances and time delays are further explored. The conditions are obtained by solving a convex optimization problem by exploring the sum of squares (SOS) of matrix polynomials and by introducing polynomially parameter-dependent Lyapunov-Krasovskii functionals (LKFs). Moreover, based on the uncertain GRNs with guaranteed disturbance attenuation, it is shown that estimates of the sought stable uncertainty sets can be obtained through a recursive strategy based on parameter-dependent Lyapunov functions and the SOS. Second, the stability conditions of GRNs described by piecewise models are considered. Depending on whether the state partitions and mode transitions are known or unknown as priori, the proposed networks are divided into two categories, i.e., switched GRNs and hybrid GRNs. It is shown that, by using common polynomial Lyapunov functions and piecewise polynomial Lyapunov functions, two conditions are established to ensure the global asymptotic stability for switched and hybrid GRNs, respectively. In addition, it is shown that, by using the SOS techniques, stability conditions in the form of LMIs for both models can be obtained. Third, the multi-stability of uncertain GRNs with multivariable regulation functions is investigated. It is shown that, by using the Lyapunov functional method and LMI technology, a criterion is established to ensure the robust asymptotical stability of the uncertain GRNs, and such condition can be extended to deal with the multi-stability problem. Moreover, it is shown that by using the square matrix representation (SMR) and by adopting polynomially parameter-dependent Lyapunov functions, a condition in the form of LMIs for robust stability for all admissible uncertainties can be obtained. Examples with synthetic and real biological models are presented in each section to illustrate the applicability and effectiveness of the theoretical results. DOI: 10.5353/th_b5089978 Subjects: Gene regulatory networks - Mathematical models Stability
Author: Mehmet Eren Ahsen
Publisher: Birkhäuser
ISBN: 3319156063
Category : Science
Languages : en
Pages : 104
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This brief examines a deterministic, ODE-based model for gene regulatory networks (GRN) that incorporates nonlinearities and time-delayed feedback. An introductory chapter provides some insights into molecular biology and GRNs. The mathematical tools necessary for studying the GRN model are then reviewed, in particular Hill functions and Schwarzian derivatives. One chapter is devoted to the analysis of GRNs under negative feedback with time delays and a special case of a homogenous GRN is considered. Asymptotic stability analysis of GRNs under positive feedback is then considered in a separate chapter, in which conditions leading to bi-stability are derived. Graduate and advanced undergraduate students and researchers in control engineering, applied mathematics, systems biology and synthetic biology will find this brief to be a clear and concise introduction to the modeling and analysis of GRNs.
Author: Xian Zhang
Publisher: Springer
ISBN: 3030170985
Category : Technology & Engineering
Languages : en
Pages : 263
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This book offers an essential introduction to the latest advances in delayed genetic regulatory networks (GRNs) and presents cutting-edge work on the analysis and design of delayed GRNs in which the system parameters are subject to uncertain, stochastic and/or parameter-varying changes. Specifically, the types examined include delayed switching GRNs, delayed stochastic GRNs, delayed reaction–diffusion GRNs, delayed discrete-time GRNs, etc. In addition, the solvability of stability analysis, control and estimation problems involving delayed GRNs are addressed in terms of linear matrix inequality or M-matrix tests. The book offers a comprehensive reference guide for researchers and practitioners working in system sciences and applied mathematics, and a valuable source of information for senior undergraduates and graduates in these areas. Further, it addresses a gap in the literature by providing a unified and concise framework for the analysis and design of delayed GRNs.
Author: Charles Thomas Baab
Publisher:
ISBN:
Category :
Languages : en
Pages : 360
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Author: J. S. Luo
Publisher:
ISBN: 9789073680159
Category :
Languages : en
Pages : 35
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Author: Feng Tyan
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ISBN:
Category :
Languages : en
Pages :
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Author: Chih-Yung Cheng
Publisher:
ISBN:
Category :
Languages : en
Pages : 288
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Author: Andres R. Takach
Publisher:
ISBN:
Category :
Languages : en
Pages : 96
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