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This book provides an authoritative introduction to the rapidly growing field of chemical reaction network theory. In particular, the book presents deep and surprising theorems that relate the graphical and algebraic structure of a reaction network to qualitative properties of the intricate system of nonlinear differential equations that the network induces. Over the course of three main parts, Feinberg provides a gradual transition from a tutorial on the basics of reaction network theory, to a survey of some of its principal theorems, and, finally, to a discussion of the theory's more technical aspects. Written with great clarity, this book will be of value to mathematicians and to mathematically-inclined biologists, chemists, physicists, and engineers who want to contribute to chemical reaction network theory or make use of its powerful results.
List of contents
Part I: Preliminaries.- Anticipating the Big Picture: Some Clues.- Chemical and Notational Preliminaries.- Reaction Networks, Kinetics, and the Induced Differential Equations.- Open Systems: Why Study Nonconservative and Otherwise Peculiar Reaction Networks?.- A Toy-Reaction-Network Zoo: Varieties of Behavior and Some Questions.- Part II: Some Principle Theorems: A First Look.- Aspects of Reaction Network Structure.- The Deficiency Zero Theorem.- Deficiency One Theory.- Concentration Robustness and Its Importance in Biology: Some More Deficiency-Oriented Theorems.- Concordant Reaction Networks: Architectures that Promote Dull, Reliable Behavior Across Broad Kinetic Classes.- The Species-Reaction Graph.- The Big Picture Revisited.- Part III: Going Deeper.- Quasi-Thermodynamic Kinetic Systems.- Detailed Balancing.- Complex Balancing.- Deficiency Zero Theory Foundations and Some Key Propositions.- Deficiency One Theory Foundations.- Concentration Robustness Foundations.- Species-Reaction Graph Foundations.
Summary
This book provides an authoritative introduction to the rapidly growing field of chemical reaction network theory. In particular, the book presents deep and surprising theorems that relate the graphical and algebraic structure of a reaction network to qualitative properties of the intricate system of nonlinear differential equations that the network induces. Over the course of three main parts, Feinberg provides a gradual transition from a tutorial on the basics of reaction network theory, to a survey of some of its principal theorems, and, finally, to a discussion of the theory’s more technical aspects. Written with great clarity, this book will be of value to mathematicians and to mathematically-inclined biologists, chemists, physicists, and engineers who want to contribute to chemical reaction network theory or make use of its powerful results.
Additional text
“This book comprehensively describes network theory applied to chemical reactions, delivering powerful conclusions surprisingly following from hypotheses that are essentially formulated in terms of linear algebra and graph theory. ... The presentation is rich in material including motivating examples, applications to practical problems, guide to the literature, and mathematical proofs. It deserves a salient place in the section on mathematical chemistry of any library.” (Dieter Erle, zbMATH 1420.92001, 2019)
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"This book comprehensively describes network theory applied to chemical reactions, delivering powerful conclusions surprisingly following from hypotheses that are essentially formulated in terms of linear algebra and graph theory. ... The presentation is rich in material including motivating examples, applications to practical problems, guide to the literature, and mathematical proofs. It deserves a salient place in the section on mathematical chemistry of any library." (Dieter Erle, zbMATH 1420.92001, 2019)
