HarmonicBalance.jl: A Julia suite for nonlinear dynamics using harmonic balance
cond-mat.mes-hall, nlin.AO, nlin.CD
Submitted: 2022-02-01
Updated: 2022-05-17
Comments: Submission to SciPost/ Resubmission to SciPost Codebases
DOI: 10.21468/SciPostPhysCodeb.6
Code: https://github.com/NonlinearOscillations/HarmonicBalance.jl
Project page: https://nonlinearoscillations.github.io/HarmonicBalance.jl/stable/examples/time_dependent
License: http://creativecommons.org/licenses/by/4.0/
The gist: HarmonicBalance.jl is a publicly available Julia package designed to simplify and solve systems of periodic time-dependent nonlinear ordinary differential equations.
Terminology
Abstract
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.
Sources
- Extracting the lifetime of a synthetic two-level system
- Limit Cycles and Chaos Induced by a Nonlinearity with Memory
- Strong parametric coupling between two ultra-coherent membrane modes
- Non-Hermitian chiral phononics through optomechanically-induced squeezing
- Roadmap on Topological Photonics
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