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Basins of Attraction for Pulse-Coupled Oscillators

Gryder, Ryan
Abstract
Basins of attraction for forward invariant sets can carve out portions of phase space where one can make predictions for asymptotic dynamics. We present com- putational algorithms for computing inner approximations of basins of attraction for discrete-time dynamical systems. The algorithms, based on subdivision tech- niques for grid construction and outer approximation of images, are adaptive and eciently allow one to identify full dimensional portions of phase space where the asymptotic dynamics may be described quantitatively. As illustration, we apply the techniques to a system of three pulse-coupled oscillators, computing an inner approximation for the basin of attraction for the synchronous (with all oscillators firing at the same time) steady state as well as a basin of attraction for a stable, non-synchronous steady state.
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2014-04-01
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https://scholarworks.wm.edu/cgi/viewcontent.cgi?article=1091&context=honorstheses&unstamped=1
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Day, Sarah
Shi, Junping
Kincaid, Rex
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Mathematics
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https://scholarworks.wm.edu/handle/internal/12669
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