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## Dynamics in State Space: One and Two Dimensions

*Robert C. Hilborn*

### in Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

- Published in print:
- 2000
- Published Online:
- January 2010
- ISBN:
- 9780198507239
- eISBN:
- 9780191709340
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507239.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The description of nonlinear behaviour using state space techniques is introduced in this chapter by examining systems with one or two dynamical variables, that is, the state spaces have one or two ... More

## Biomolecular Feedback Systems

*Domitilla Del Vecchio and Richard M. Murray*

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161532
- eISBN:
- 9781400850501
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161532.001.0001
- Subject:
- Biology, Biochemistry / Molecular Biology

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 ... More

## The Tunable Brain

*Mari Riess Jones*

### in Time Will Tell: A Theory of Dynamic Attending

- Published in print:
- 2019
- Published Online:
- January 2019
- ISBN:
- 9780190618216
- eISBN:
- 9780190618230
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190618216.003.0003
- Subject:
- Psychology, Cognitive Psychology, Music Psychology

This chapter introduces some elementary entrainment concepts such as phase space, phase portrait, bifurcation, and attractors. Limit cycle oscillations are introduced. It also provides a simplified ... More

## Nonlinear Dynamics and Chaos

*David D. Nolte*

### in Introduction to Modern Dynamics: Chaos, Networks, Space, and Time

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198844624
- eISBN:
- 9780191880216
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198844624.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The geometric structure of state space is understood through phase portraits and stability analysis that classify the character of fixed points based on the properties of Lyapunov exponents. Limit ... More

## Two‐Dimensional Differential Equations

*David P. Feldman*

### in Chaos and Fractals: An Elementary Introduction

- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199566433
- eISBN:
- 9780191774966
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199566433.003.0031
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter deals with two-dimensional differential equations and examines whether they are capable of a richer set of behaviours compared with their one-dimensional counterparts. It begins by ... More

## Self-Assembly and Beyond

*Troy Shinbrot*

### in Biomedical Fluid Dynamics: Flow and Form

- Published in print:
- 2019
- Published Online:
- June 2019
- ISBN:
- 9780198812586
- eISBN:
- 9780191850721
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198812586.003.0013
- Subject:
- Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Effects of combining reaction with diffusion are examined, and the resulting self-assembly of ordered patterns is overviewed. Turing patterns and limit cycle oscillations are shown to result from ... More

## Dynamical systems on networks

*Mark Newman*

### in Networks

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198805090
- eISBN:
- 9780191843235
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805090.003.0017
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

An introduction to the theory of dynamical systems on networks. This chapter starts with a short introduction to classical (non-network) dynamical systems theory, including linear stability analysis, ... More

## Conclusion

*Wassim M. Haddad and Sergey G. Nersesov*

### in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691153469
- eISBN:
- 9781400842667
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153469.003.0014
- Subject:
- Mathematics, Applied Mathematics

This book has described a general stability analysis and control design framework for large-scale dynamical systems, with an emphasis on vector Lyapunov function methods, vector dissipativity theory, ... More

## Coupled Oscillators

*Irving R. Epstein and John A. Pojman*

### in An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos

- Published in print:
- 1998
- Published Online:
- November 2020
- ISBN:
- 9780195096705
- eISBN:
- 9780197560815
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195096705.003.0018
- Subject:
- Chemistry, Physical Chemistry

We have thus far learned a great deal about chemical oscillators, but, except in Chapter 9, where we looked at the effects of external fields, our ... More

## Predator-Prey Interactions

*Peter A. Abrams*

### in Evolutionary Ecology: Concepts and Case Studies

- Published in print:
- 2001
- Published Online:
- November 2020
- ISBN:
- 9780195131543
- eISBN:
- 9780197561461
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195131543.003.0028
- Subject:
- Environmental Science, Applied Ecology

Predation has been given many different definitions. For the purposes of this chapter, it is an interaction in which one free-living individual kills and ... More

## Analysis of Chemical Oscillations

*Irving R. Epstein and John A. Pojman*

### in An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos

- Published in print:
- 1998
- Published Online:
- November 2020
- ISBN:
- 9780195096705
- eISBN:
- 9780197560815
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195096705.003.0010
- Subject:
- Chemistry, Physical Chemistry

Many of the most remarkable achievements of chemical science involve either synthesis (the design and construction of molecules) or analysis (the ... More

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