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## Mathematical and computational modelling tools

*Baltazar D. Aguda and Avner Friedman*

### in Models of Cellular Regulation

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198570912
- eISBN:
- 9780191718717
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570912.003.0003
- Subject:
- Physics, Soft Matter / Biological Physics

This chapter reviews chemical kinetics to illustrate the formulation of model equations for a given reaction mechanism. For spatially uniform systems, these model equations are usually ordinary ... More

## Differential equations in physics

*Chun Wa Wong*

### in Introduction to Mathematical Physics: Methods & Concepts

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199641390
- eISBN:
- 9780191747786
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199641390.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Ordinary and partial differential equations appear in physics as equations of motion or of state. They are often linear differential equations for which a sum of solutions remains a solution. The ... More

## Differential Equations

*Bard Ermentrout and John Rinzel*

### in Computational Modeling Methods for Neuroscientists

- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262013277
- eISBN:
- 9780262258722
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262013277.003.0002
- Subject:
- Neuroscience, Techniques

This chapter, which addresses the partial differential equations (PDEs) with the example of finding the speed and profile of a propagating impulse for a Hodgkin-Huxley-like cable equation, highlights ... More

## Ordinary differential equations

*Joseph F. Boudreau and Eric S. Swanson*

### in Applied Computational Physics

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198708636
- eISBN:
- 9780191858598
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198708636.003.0011
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter surveys the ordinary differential equations (ODEs) that occur in classical and quantum mechanics, and describes both numerical algorithms and appropriate software design for solving ... More

## Ordinary Differential Equations

*Thomas A. Weber*

### in Optimal Control Theory with Applications in Economics

- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015738
- eISBN:
- 9780262298483
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015738.003.0002
- Subject:
- Mathematics, Probability / Statistics

This chapter reviews basic concepts in the theory of ordinary differential equation (ODEs). It first discusses how to analyze first-order ODEs. It then extends the framework for the analysis of ... More

## Optimal Control Theory with Applications in Economics

*Thomas A. Weber*

- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015738
- eISBN:
- 9780262298483
- Item type:
- book

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015738.001.0001
- Subject:
- Mathematics, Probability / Statistics

This book bridges optimal control theory and economics, discussing ordinary differential equations (ODEs), optimal control, game theory, and mechanism design in one volume. Technically rigorous and ... More

## A Primer on Control Engineering

*Brian P. Ingalls and Pablo A. Iglesias*

### in Control Theory and Systems Biology

- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262013345
- eISBN:
- 9780262258906
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262013345.003.0001
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

This chapter addresses the main concepts in this book from dynamical systems and control theory, introducing ordinary differential equation-based modeling, which should allow theoretically inclined ... More

## An introduction to modeling the initiation of the floral primordium

*Christophe Godin, Eugenio Azpeitia, and Etienne Farcot*

### in From Molecules to Living Organisms: An Interplay Between Biology and Physics: Lecture Notes of the Les Houches School of Physics: Volume 102, July 2014

- Published in print:
- 2016
- Published Online:
- March 2016
- ISBN:
- 9780198752950
- eISBN:
- 9780191814426
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198752950.003.0009
- Subject:
- Physics, Soft Matter / Biological Physics

This chapter presents models of processes involved in the initiation and development of a flower. Models of hormonal transport are briefly described, focusing on two key aspects of floral ... More

## Basic Predictor Feedback for Single-Input Systems

*Yang Zhu and Miroslav Krstic*

### in Delay-Adaptive Linear Control

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691202549
- eISBN:
- 9780691203317
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691202549.003.0002
- Subject:
- Mathematics, Applied Mathematics

This chapter discusses the basic idea of a partial differential equation (PDE) backstepping approach for single-input LTI ordinary differential equation (ODE) systems with discrete input delay. The ... More

## Empirically Detecting Causality

*Ray Huffaker, Marco Bittelli, and Rodolfo Rosa*

### in Nonlinear Time Series Analysis with R

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198782933
- eISBN:
- 9780191826153
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198782933.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Phenomenological models mathematically describe relationships among empirically observed phenomena without attempting to explain underlying mechanisms. Within the context of NLTS, phenomenological ... More

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