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Paper detail

The Algebraic Degree of Coupled Oscillators

Approximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic complexity of this approximation problem. Using the theory of Khovanskii bases, we show that this number is given by the volume of a certain polytope. We also show how to compute all solutions using numerical nonlinear algebra.

preprint2022arXivOpen access
Paul BreidingMateusz MichałekLeonid MoninSimon Telen
math.AG
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Paul BreidingMateusz MichałekLeonid MoninSimon Telen

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