Analysis and control of polynomial dynamic models with biological applications. ([2018])

• Record Type: Book
• Further Information: Note: Attila Magyar, Gábor Szederkényi, Katalin M. Hangos.
• Authors: Magyar, Attila; Szederkényi, G (Gàbor), 1975-; Hangos, K. M (Katalin M.)
• 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 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 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 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 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
• Publisher Details: London, United Kingdom : Elsevier Ltd Academic Press
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 003/.75; Nonlinear systems; Polynomials; SCIENCE / System Theory; TECHNOLOGY & ENGINEERING / Operations Research; Electronic books
• Languages: English
• ISBNs: 9780128154960; 0128154969
• Related ISBNs: 9780128154953
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed April 6, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.