HarmonicBalance.jl: A Julia suite for nonlinear dynamics using harmonic balance

arXiv:2202.00571 · cond-mat.mes-hall, nlin.AO, nlin.CD · Submitted 2022-02-01 · Read on arXiv

cond-mat.mes-hall, nlin.AO, nlin.CD

Submitted: 2022-02-01

Updated: 2022-05-17

Code: https://github.com/NonlinearOscillations/HarmonicBalance.jl

Project page: https://nonlinearoscillations.github.io/HarmonicBalance.jl/stable/examples/time_dependent

Terminology

• Limit Cycles — 5× in this paper · explained in 2 episodes
• Core — 4× in this paper · explained in 2 episodes
• Hysteresis — 2× in this paper · explained in 3 episodes
• Symmetry Breaking — 2× in this paper · explained in 3 episodes
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Computational overhead — 1× in this paper · explained in 2 episodes
• Effective Hamiltonian — 1× in this paper · explained in 2 episodes
• Floquet Engineering — 1× in this paper · explained in 3 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Magnus Expansion — 1× in this paper · explained in 4 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• System Identification — 1× in this paper · explained in 3 episodes
• Trace — 1× in this paper · explained in 2 episodes

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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