Installation

using PkgPkg.add("HarmonicBalance")

Documentation

Example: steady states of a nonlinear resonator

using HarmonicBalance, Plots@variables α ω ω0 F η tx(t)# declare constant variables and a function x(t)diff_eq=DifferentialEquation(d(x,t,2)+ ω0^2*x+ α*x^3+ η*d(x,t)*x^2~ F*cos(ω*t), x)add_harmonic!(diff_eq, x, ω)# specify the ansatz x = u(T) cos(ωt) + v(T) sin(ωt)# implement ansatz to get harmonic equationsharmonic_eq=get_harmonic_equations(diff_eq)# solve for a range of ωresult=get_steady_states(harmonic_eq, ω=>range(0.9,1.2,100), (α=>1., ω0=>1.0, F=>0.01, η=>0.1))

A steady state result for 100 parameter pointsSolution branches:   3   of which real:    3   of which stable:  2Classes: stable, physical, Hopf, binary_labels

plot(result,"sqrt(u1^2 + v1^2)")

Citation

BibTeX entry

@Article{10.21468/SciPostPhysCodeb.6,title={{HarmonicBalance.jl: A Julia suite for nonlinear dynamics using harmonic balance}},author={Jan Košata and Javier del Pino and Toni L. Heugel and Oded Zilberberg},journal={SciPost Phys. Codebases},pages={6},year={2022},publisher={SciPost},doi={10.21468/SciPostPhysCodeb.6},url={https://scipost.org/10.21468/SciPostPhysCodeb.6}}

See also