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I co-develop HarmonicBalance.jl, a Julia package for solving nonlinear differential equations using the method of harmonic balance.

HarmonicBalance.jl

I co-develop HarmonicBalance.jl with Orjan Ameye and Jan Košata.

HarmonicBalance.jl is a Julia package for studying nonlinear, periodically driven systems in the frequency domain. It combines harmonic balance with homotopy continuation to find steady states and periodic solutions without relying on repeated time evolution from different initial conditions.

Key features

  • Map phase diagrams across multiple parameters.
  • Find and analyse coexisting steady states and limit cycles.
  • Study stability and fluctuation dynamics.
  • Connect symbolic equations with numerical continuation tools.

GitHub repository · Documentation · SciPost paper

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The package is open source and welcomes contributions.