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A System of Rhythms: From Simple to Complex Dynamics

Buzsáki György

in Rhythms of the Brain

Published in print:
2006
Published Online:
May 2009
ISBN:
9780195301069
eISBN:
9780199863716
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195301069.003.0005
Subject:
Neuroscience, Neuroendocrine and Autonomic, Techniques

Neuronal networks in the mammalian cortex generate several distinct oscillatory bands. These neuronal oscillators are linked to the much slower metabolic oscillators. The mean frequencies of the ... More


Measures of EEG Dynamic Properties

Paul L. Nunez and Ramesh Srinivasan

in Electric Fields of the Brain: The neurophysics of EEG

Published in print:
2006
Published Online:
May 2009
ISBN:
9780195050387
eISBN:
9780199865673
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195050387.003.0009
Subject:
Neuroscience, Neuroendocrine and Autonomic, Techniques

This chapter suggests a general working framework for experimental study of large-scale dynamics of EEG, including interpretation of data recorded at different spatial and temporal scales. It views ... More


Coupled Oscillators and Synchronization

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/9780198844624.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Coupled linear oscillators provide a central paradigm for the combined behavior of coupled systems and the emergence of normal modes. Nonlinear coupling of two autonomous oscillators provides an ... More


Pattern Formation and Spatiotemporal Chaos

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/9780198507239.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

When a dynamical system has significant spatial extent, its nonlinear dynamics can lead to the spontaneous formation of spatial patterns. Such systems provide models for how nature might have ... More


Coupled Oscillators

Helmut Satz

in The Rules of the Flock: Self-Organization and Swarm Structure in Animal Societies

Published in print:
2020
Published Online:
March 2020
ISBN:
9780198853398
eISBN:
9780191888052
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853398.003.0010
Subject:
Physics, Soft Matter / Biological Physics, Particle Physics / Astrophysics / Cosmology

Pendulums on a common basis become eventually synchronized, through transmission of swing frequency. Coupled electric oscillators show the same effect. The application of this effect to synchronized ... More


Canonical transformations

Gleb L. Kotkin and Valeriy G. Serbo

in Exploring Classical Mechanics: A Collection of 350+ Solved Problems for Students, Lecturers, and Researchers - Second Revised and Enlarged English Edition

Published in print:
2020
Published Online:
October 2020
ISBN:
9780198853787
eISBN:
9780191888236
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853787.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

This chapter addresses the canonical transformation defined by the given generating function, the rotation in the phase space as a canonical transformation, and themovement of the system as a ... More


Canonical transformations

Gleb L. Kotkin and Valeriy G. Serbo

in Exploring Classical Mechanics: A Collection of 350+ Solved Problems for Students, Lecturers, and Researchers - Second Revised and Enlarged English Edition

Published in print:
2020
Published Online:
October 2020
ISBN:
9780198853787
eISBN:
9780191888236
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853787.003.0024
Subject:
Physics, Condensed Matter Physics / Materials

This chapter addresses the canonical transformation defined by the given generating function, the rotation in the phase space as a canonical transformation, and themovement of the system as a ... More


Mechanics of Molecules

F. Iachello and R. D. Levine

in Algebraic Theory of Molecules

Published in print:
1995
Published Online:
November 2020
ISBN:
9780195080919
eISBN:
9780197560419
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195080919.003.0006
Subject:
Chemistry, Physical Chemistry

Triatomic molecules The Hamiltonian of a triatomic molecule in the Born–Oppenheimer approximation is [math] where mi is the mass of the ith atom....


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