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arXiv · 2208.08179

The Algebraic Degree of Coupled Oscillators

Paul Breiding·Mateusz Michałek·Leonid Monin·Simon Telen
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Abstract

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.

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Paul Breiding, Mateusz Michałek, Leonid Monin, Simon Telen. 2022-08-17. The Algebraic Degree of Coupled Oscillators. https://arxiv.org/abs/2208.08179

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