Jan Kovsata, J. Pino, Toni L. Heugel, O. Zilberberg
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HarmonicBalance.jl: A Julia suite for nonlinear dynamics using harmonic balance
HarmonicBalance.jl is a publicly available Julia package designed to
simplify and solve systems of periodic time-dependent nonlinear ordinary
differential equations. Time dependence of the system parameters is
treated with the harmonic balance method, which approximates the
system’s behaviour as a set of harmonic terms with slowly-varying
amplitudes. Under this approximation, the set of all possible
steady-state responses follows from the solution of a polynomial system.
In HarmonicBalance.jl, we combine harmonic balance with contemporary
implementations of symbolic algebra and the homotopy continuation method
to numerically determine all steady-state solutions and their associated
fluctuation dynamics. For the exploration of involved steady-state
topologies, we provide a simple graphical user interface, allowing for
arbitrary solution observables and phase diagrams. HarmonicBalance.jl is
a free software available at https://github.com/NonlinearOscillations/HarmonicBalance.jl.