Publication

The algebraic degree of coupled oscillators

2025

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 polytope. We also show how to compute all solutions using numerical nonlinear algebra.

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The algebraic degree of coupled oscillators

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Numerical modelling of potential and current distributions in a bipolar electrolytic cell