Date Thesis Awarded

7-2012

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Sarah Day

Committee Member

M. Drew Lamar

Committee Member

Gregory D. Smith

Committee Member

Rex K. Kincaid

Abstract

Networks of pulse-coupled oscillators can be used to model systems from firing neurons to blinking fireflies. Many past studies have focused on numerical simulations and locating the synchronous state of such systems. In this project, we construct a Poincare map for a system of three pulse-coupled oscillators and use rigorous computational techniques and topological tools to study both synchronous and asynchronous dynamics. We present sample results, including the computed basin of attraction for the synchronous state as well as a depiction of gradient-like dynamics in the remainder of the phase space. In the future, we hope to automate this process so that it can be applied to a wide range of network topologies and parameter values.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

Comments

Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.

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