HarmonicBalance。使用谐波平衡的非线性动力学Julia套件

Jan Kovsata, J. Pino, Toni L. Heugel, O. Zilberberg
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引用次数: 7

摘要

HarmonicBalance。jl是一个公开可用的Julia包,旨在简化和求解周期时相关非线性常微分方程系统。用谐波平衡法处理系统参数的时间依赖性,该方法将系统的行为近似为一组振幅缓慢变化的谐波项。在这种近似下,所有可能的稳态响应的集合由多项式系统的解得出。在HarmonicBalance。最后,我们将谐波平衡与符号代数的现代实现和同伦延拓方法相结合,在数值上确定了所有稳态解及其相关的涨落动力学。对于所涉及的稳态拓扑的探索,我们提供了一个简单的图形用户界面,允许任意解决观测和相位图。HarmonicBalance。jl是免费软件,可从https://github.com/NonlinearOscillations/HarmonicBalance.jl获得。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
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