| Description |
1 online resource |
| Contents |
Front Cover; Analysis and Control of Polynomial Dynamic Models with Biological Applications; Copyright; Dedication; Contents; About the Authors; Preface; Acknowledgments; Chapter 1: Introduction; 1.1 Dynamic Models for Describing Biological Phenomena; 1.2 Kinetic Systems; 1.2.1 Chemical Reaction Networks With Mass Action Law; 1.2.2 Chemical Reaction Networks With Rational Functions as Reaction Rates; 1.3 QP Models; 1.3.1 Original Lotka-Volterra Equations; 1.3.2 Generalized Lotka-Volterra Equations; Chapter 2: Basic Notions |
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2.1 General Nonlinear System Representation in the Form of ODEs2.1.1 Autonomous Polynomial and Quasipolynomial Systems; 2.1.1.1 Polynomial Systems; 2.1.1.2 Quasipolynomial Systems; 2.1.1.3 Extension With Input Terms; 2.1.2 Positive Polynomial Systems; 2.2 Formal Introduction of the QP Model Form; 2.2.1 QP Model Form; 2.2.1.1 Compact Matrix-Vector Forms of QP Models; 2.2.1.2 An Entropy-Like Lyapunov Function Candidate for QP Models; 2.2.2 LV Systems; 2.2.3 Extension With Input Term; 2.3 Introduction of Kinetic Models With Mass Action and Rational Reaction Rates |
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2.3.1 General Notions for Reaction Networks2.3.1.1 Reaction Graph; 2.3.1.2 Important Structural Properties of Reaction Networks; 2.3.2 Reaction Networks With Mass Action Kinetics; 2.3.2.1 The Reaction Graph of Mass Action Networks; 2.3.2.2 Important Properties of Mass Action-Type Reaction Networks and Their Implications; 2.3.3 Kinetic Realizability and Structural Nonuniqueness of Mass Action-Type Reaction Networks; 2.3.3.1 Procedure for Computing a Canonical Mechanism; 2.3.3.2 Dynamic Equivalence; 2.3.4 Reaction Networks With Rational Function Kinetics; 2.3.4.1 Reaction Graph |
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2.3.4.2 Dynamical Equations of Bio-CRNs2.3.4.3 Network Realization and Dynamical Equivalence; 2.3.5 Extension With Input Term; 2.4 Basic Relations Between Kinetic and QP Models; 2.4.1 Representing Kinetic Models With Mass Action Reaction Rates as QP Models; 2.4.2 LV Models as Kinetic Systems; Chapter 3: Model Transformations and Equivalence Classes; 3.1 Affine and Linear Positive Diagonal Transformations; 3.1.1 Affine Transformations and Their Special Cases for Positive Polynomial Systems; 3.1.2 Positive Diagonal Transformation of QP Systems |
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3.1.3 Positive Diagonal Transformation of CRNs: Linear Conjugacy3.1.3.1 Linear Conjugacy of Networks With Mass Action Kinetics; 3.1.3.2 Linear Conjugacy of CRNs With Rational Reaction Rates; 3.2 Nonlinear Diagonal Transformations; 3.2.1 X-Factorable Transformation; 3.2.2 State-Dependent Time-Rescaling; 3.2.2.1 Time-Rescaling Transformation of QP Models; 3.3 Quasimonomial Transformation and the Corresponding Equivalence Classes of QP Systems; 3.3.1 Quasimonomial Transformation (QM Transformation); 3.3.2 The Lotka-Volterra (LV) Form and the Invariants |
| Summary |
Analysis and Control of Polynomial Dynamic Models with Biological Applications synthesizes three mathematical background areas (graphs, matrices and optimization) to solve problems in the biological sciences (in particular, dynamic analysis and controller design of QP and polynomial systems arising from predator-prey and biochemical models). The book puts a significant emphasis on applications, focusing on quasi-polynomial (QP, or generalized Lotka-Volterra) and kinetic systems (also called biochemical reaction networks or simply CRNs) since they are universal descriptors for smooth nonlinear systems and can represent all important dynamical phenomena that are present in biological (and also in general) dynamical systems |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (EBSCO, viewed April 6, 2018) |
| Subject |
Nonlinear systems.
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Polynomials.
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Mathematics.
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Biological models.
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Mathematics
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Models, Biological
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Nonlinear Dynamics
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SCIENCE -- System Theory.
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TECHNOLOGY & ENGINEERING -- Operations Research.
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Mathematics
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Biological models
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Nonlinear systems
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Polynomials
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| Form |
Electronic book
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| Author |
Szederkényi, G. (Gàbor), 1975- author.
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Hangos, K. M. (Katalin M.), author.
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| ISBN |
9780128154960 |
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0128154969 |
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