Urban, Alexander
(2012)
Intermediate Stable Phase Locked States In Oscillator Networks.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
The study of nonlinear oscillations is important in a variety of physical and biological contexts (especially in neuroscience).
Synchronization of oscillators has been a problem of interest in recent years. In networks of nearest neighbor coupled oscillators it is possible to obtain synchrony between oscillators, but also a variety of constant phase shifts between 0 and pi. We coin these phase shifts intermediate stable phase-locked states. In neuroscience, both individual neurons and populations of neurons can behave as complex nonlinear oscillators.
Intermediate stable phase-locked states are shown to be obtainable between individual oscillators and populations of identical oscillators.These intermediate stable phase-locked states may be useful in the construction of central pattern generators: autonomous neural cicuits responsible for motor behavior. In large chains and two-dimenional arrays of oscillators, intermediate stable phase-locked states provide a mechanism to produce waves and patterns that cannot be obtained in traditional network models. A particular pattern of interest is known as an anti-wave. This pattern corresponds to the collision of two waves from opposite ends of an oscillator chain. This wave may be relevant in the spinal central pattern generators of various fish. Anti-wave solutions in both conductance based neuron models and phase oscillator models are analyzed. It is shown that such solutions arise in phase oscillator models in which the nonlinearity (interaction function) contains both higher order odd and even Fourier modes. These modes are prominent in pairs of synchronous oscillators which lose stability in a supercritical pitchfork bifurcation.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
| Title | Member | Email Address | Pitt Username | ORCID |
|---|
| Committee Chair | Jasnow, David | | | | | Committee CoChair | Ermentrout, Bard | | | | | Committee Member | Coalson, Rob | | | | | Committee Member | Wu, Xiao Lun | | | | | Committee Member | Boudreau, Joe | | | |
|
| Date: |
1 February 2012 |
| Date Type: |
Publication |
| Defense Date: |
21 July 2011 |
| Approval Date: |
1 February 2012 |
| Submission Date: |
5 December 2011 |
| Access Restriction: |
2 year -- Restrict access to University of Pittsburgh for a period of 2 years. |
| Number of Pages: |
206 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Physics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Nonlinear Dynamics, Computational Physics, Biological Physics, Theoretical Neuroscience |
| Date Deposited: |
01 Feb 2012 15:02 |
| Last Modified: |
15 Nov 2016 13:55 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/10659 |
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