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Global Dynamics of Pulse-Coupled Oscillators

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Author: Corish, Allison Leslie
Advisor: Day, Sarah, 1975-
Committee Members: Lamar, M. Drew; Smith, Gregory D.; Kincaid, Rex K.
Issued Date: 7/13/2012
Subjects: Conley index
Dynamical systems
Algebraic topology
Pulse-coupled oscillators
URI: http://hdl.handle.net/10288/16706
Description: 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.
Degree: Bachelors of Science in Mathematics

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