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Cyclic Feedback Systems

Author: Tomáš Gedeon

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 89

ISBN-13: 0821807838

Explores the global dynamics of a class of ordinary differential equations called cyclic feedback systems. The global dynamics is described by a Morse decomposition of the global attractor, defined with the help of a discrete Lyapunov function. A three-dimensional system of ODE's with two linear equations is constructed, such that the invariant set is at least as complicated as a suspension of a full shift on two symbols. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Feedback Systems

Author: Karl Johan Åström

Publisher: Princeton University Press

Published: 2021-02-02

Total Pages:

ISBN-13: 069121347X

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The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory

Biomolecular Feedback Systems

Author: Domitilla Del Vecchio

Publisher: Princeton University Press

Published: 2014-10-26

Total Pages: 286

ISBN-13: 0691161534

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This book provides an accessible introduction to the principles and tools for modeling, analyzing, and synthesizing biomolecular systems. It begins with modeling tools such as reaction-rate equations, reduced-order models, stochastic models, and specific models of important core processes. It then describes in detail the control and dynamical systems tools used to analyze these models. These include tools for analyzing stability of equilibria, limit cycles, robustness, and parameter uncertainty. Modeling and analysis techniques are then applied to design examples from both natural systems and synthetic biomolecular circuits. In addition, this comprehensive book addresses the problem of modular composition of synthetic circuits, the tools for analyzing the extent of modularity, and the design techniques for ensuring modular behavior. It also looks at design trade-offs, focusing on perturbations due to noise and competition for shared cellular resources. Featuring numerous exercises and illustrations throughout, Biomolecular Feedback Systems is the ideal textbook for advanced undergraduates and graduate students. For researchers, it can also serve as a self-contained reference on the feedback control techniques that can be applied to biomolecular systems. Provides a user-friendly introduction to essential concepts, tools, and applications Covers the most commonly used modeling methods Addresses the modular design problem for biomolecular systems Uses design examples from both natural systems and synthetic circuits Solutions manual (available only to professors at press.princeton.edu) An online illustration package is available to professors at press.princeton.edu

Biomolecular Feedback Systems

Author: Domitilla Del Vecchio

Publisher: Princeton University Press

Published: 2014-10-26

Total Pages: 287

ISBN-13: 1400850509

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Dynamics of Feedback Systems

Author: A. I. Mees

Publisher: John Wiley & Sons

Published: 1981

Total Pages: 234

ISBN-13:

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Biological Clocks, Rhythms, and Oscillations

Author: Daniel B. Forger

Publisher: MIT Press

Published: 2017-11-16

Total Pages: 369

ISBN-13: 0262036770

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An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications. All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical, computational, and analytical techniques used for modeling biological rhythms, gathering these methods for the first time in one volume. Drawing on material from such disciplines as mathematical biology, nonlinear dynamics, physics, statistics, and engineering, it presents practical advice and techniques for studying biological rhythms, with a common language. The chapters proceed with increasing mathematical abstraction. Part I, on models, highlights the implicit assumptions and common pitfalls of modeling, and is accessible to readers with basic knowledge of differential equations and linear algebra. Part II, on behaviors, focuses on simpler models, describing common properties of biological rhythms that range from the firing properties of squid giant axon to human circadian rhythms. Part III, on mathematical techniques, guides readers who have specific models or goals in mind. Sections on “frontiers” present the latest research; “theory” sections present interesting mathematical results using more accessible approaches than can be found elsewhere. Each chapter offers exercises. Commented MATLAB code is provided to help readers get practical experience. The book, by an expert in the field, can be used as a textbook for undergraduate courses in mathematical biology or graduate courses in modeling biological rhythms and as a reference for researchers.

Time Delay Systems

Author: Tamás Insperger

Publisher: Springer

Published: 2017-03-30

Total Pages: 362

ISBN-13: 3319534262

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This volume collects contributions related to selected presentations from the 12th IFAC Workshop on Time Delay Systems, Ann Arbor, June 28-30, 2015. The included papers present novel techniques and new results of delayed dynamical systems. The topical spectrum covers control theory, numerical analysis, engineering and biological applications as well as experiments and case studies. The target audience primarily comprises research experts in the field of time delay systems, but the book may also be beneficial for graduate students alike.

Geochemistry of Earth Surface Systems

Author: Heinrich D Holland

Publisher: Academic Press

Published: 2010-09-27

Total Pages: 689

ISBN-13: 0080967078

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Geochemistry of Earth Surface Systems offers an interdisciplinary reference for scientists, researchers and upper undergraduate and graduate level geochemistry students a sampling of articles on earth surface processes from The Treatise on Geochemistry that is more affordable than the full Treatise. For professionals, this volume will provide an overview of the field as a whole. For students, it will provide more in-depth introductory content than is found in broad-based geochemistry textbooks. Articles were selected from chapters across all volumes of the full Treatise, and include: Volcanic Degassing, Hydrothermal Processes, The Contemporary Carbon Cycle, Global Occurrence of Major Elements in Rivers, Organic Matter in the Contemporary Ocean, The Biological Pump, and Evolution of Sedimentary Rocks. Comprehensive, interdisciplinary and authoritative content selected by leading subject experts Robust illustrations, figures and tables Affordably priced sampling of content from the full Treatise on Geochemistry

Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems

Author: Hal L. Smith

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 186

ISBN-13: 0821844873

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This book presents comprehensive treatment of a rapidly developing area with many potential applications: the theory of monotone dynamical systems and the theory of competitive and cooperative differential equations. The primary aim is to provide potential users of the theory with techniques, results, and ideas useful in applications, while at the same time providing rigorous proofs. Among the topics discussed in the book are continuous-time monotone dynamical systems, and quasimonotone and nonquasimonotone delay differential equations. The book closes with a discussion of applications to quasimonotone systems of reaction-diffusion type. Throughout the book, applications of the theory to many mathematical models arising in biology are discussed. Requiring a background in dynamical systems at the level of a first graduate course, this book is useful to graduate students and researchers working in the theory of dynamical systems and its applications.

The Cell Cycle

Author: David Owen Morgan

Publisher: New Science Press

Published: 2007

Total Pages: 328

ISBN-13: 0878935088

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The Cell Cycle: Principles of Control provides an engaging insight into the process of cell division, bringing to the student a much-needed synthesis of a subject entering a period of unprecedented growth as an understanding of the molecular mechanisms underlying cell division are revealed.