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Intermediate Stable Phase Locked States In Oscillator Networks

Urban, Alexander (2012) Intermediate Stable Phase Locked States In Oscillator Networks. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairJasnow, David
Committee CoChairErmentrout, Bard
Committee MemberCoalson, Rob
Committee MemberWu, Xiao Lun
Committee MemberBoudreau, 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


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