Orr, Derek
(2021)
How Oscillations persist through chains of Excitable cells and in large noise-driven Excitable systems.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Our goal is to understand how excitable cells and oscillatory cells interact with each other and, ultimately, decide if excitable cells can generate macroscopic oscillations that persist in these networks. We begin by studying a one-dimensional chain model of this: oscillatory cells coupled indirectly with excitable cells in between. We have three main systems: OE, OEO, and OEEO. We show that with the right coupling strength, one can get the two oscillators on the ends to synchronize (or not synchronize) and the system exhibits $m$:$n$ locking patterns.
In our second project, we remove the chain constraint and focus on just all-to-all coupled excitable cells. However, these will not create oscillations alone so we added noise to these cells so the cells can oscillate randomly in the network. We perform mean-field theory (MFT) methods on this system and chose Gaussian white noise as well as different heterogeneous noise distributions. We find that macroscopic oscillations can occur as long as one has the right set of parameters, the right noise distribution, and/or the right coupling function.
In the final project, we combine the first two projects: we take the noisy excitable cells, which we know can create oscillations, and we couple each cell to a single oscillator. When the noise level is zero, this is equivalent to one oscillator and one excitable cell coupled to each other (our OE model from the first project). Hence, we find $m$:$n$ locking patterns again. This last project investigates how large the noise level can become before the $m$:$n$ locking patterns become unstable. We notice that using heterogeneous noise allows for the noise threshold to be larger than when using Gaussian noise.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
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| ETD Committee: |
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| Date: |
3 May 2021 |
| Date Type: |
Publication |
| Defense Date: |
16 March 2021 |
| Approval Date: |
3 May 2021 |
| Submission Date: |
3 April 2021 |
| Access Restriction: |
2 year -- Restrict access to University of Pittsburgh for a period of 2 years. |
| Number of Pages: |
116 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
oscillators, ott-antonsen ansatz, mean field theory, pattern formation |
| Date Deposited: |
03 May 2021 15:13 |
| Last Modified: |
03 May 2023 05:15 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/40503 |
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