Marella, Sashi
(2012)
Stochastic Synchrony and Phase Resetting Curves: Theory and Applications.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
In this thesis, our goal was to study the phase synchronization between two uncoupled oscillators receiving partially correlated input. Using perturbation methods we obtain a closed-form solution for the steady-state density of phase differences between the two oscillators. Order parameters for synchrony and cross-correlation are used to quantify the degree of stochastic synchronization. We show that oscillators proscribed with Type-II phase resetting curves (PRC's) are more prone to stochastic synchronization compared to Type-I PRCs, and that the synchrony in the system can be described by a closed-form expression for the probability distribution of phase differences between the two uncoupled oscillators. We also study Morris-Lecar, leaky integrate-and-fire model and the Wang-Buzsaki
interneuron model. Motivated by our theoretical developments, we study synchronization in simple neuronal network models of the olfactory bulb by applying the results from the theoretical studies to spiking neuron models with feedback to qualitatively demonstrate the emergence of self-organized synchrony. Here we again use an abstract model to obtain an
expression for the averaged dynamics and compare our predicted solutions using Monte-Carlo simulations. We also show that an arbitrary mechanism that has a finite time memory of correlated inputs can cause bistability in such a system. Furthermore, we investigated the rate at which such systems approach their steady-state distribution and show that the dependence of the rate on the shape of the PRC. We obtained an expression for the rate of convergence to the steady-state
density of phase differences in a two oscillators system receiving partially correlated inputs
without feedback. To this end, we study the closed-form expression to obtain an
approximation using a perturbation technique suited for computing large eigenvalues. It is shown that Type-II PRC's converge to their steady-state density compared to Type-I PRC's and that the rate of convergence is dependent on the input correlation. Our theoretical and numerical studies suggest a potential mechanism by which asynchronous inhibtion may promote and amplify synchronization in systems where the individual actors can be described as general oscillators at least in certain regimes of their activity with a possible source of activity dependent and partially correlated feedback.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
29 June 2012 |
| Date Type: |
Publication |
| Defense Date: |
2 May 2011 |
| Approval Date: |
29 June 2012 |
| Submission Date: |
21 March 2012 |
| Access Restriction: |
5 year -- Restrict access to University of Pittsburgh for a period of 5 years. |
| Number of Pages: |
87 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Neuroscience |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Stochastic synchrony, Phase resetting curve, Olfactory bulb, Brain |
| Date Deposited: |
29 Jun 2012 17:13 |
| Last Modified: |
29 Jun 2017 05:15 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/11514 |
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