2025-08-22
The algebraic degree of coupled oscillators
Publication
Publication
Advances in Mathematics , Volume 480
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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| , , , , | |
| doi.org/10.1016/j.aim.2025.110492 | |
| Advances in Mathematics | |
| New frontiers in numerical nonlinear algebra | |
| Organisation | Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands |
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Breiding, P., Michalek, M., Monin, L., & Telen, S. J. L. (2025). The algebraic degree of coupled oscillators. Advances in Mathematics, 480. doi:10.1016/j.aim.2025.110492 |
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