论文标题
Harmonicalance.jl：使用谐波平衡的朱莉娅套件用于非线性动力学
HarmonicBalance.jl: A Julia suite for nonlinear dynamics using harmonic balance
论文作者
论文摘要
HarmonicBalance.jl是一种公开可用的Julia软件包，旨在简化和解决定期时间依赖性非线性普通微分方程的系统。使用谐波平衡方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谐波项，并具有缓慢变化的幅度。在此近似值下，所有可能的稳态响应的集合都遵循多项式系统的解决方案。在谐波中，我们将谐波平衡与符号代数的当代实现相结合，以及同型连续方法，以确定所有稳态解决方案及其相关的波动动态。为了探索所涉及的稳态拓扑结构，我们提供了一个简单的图形用户界面，允许使用任意的解决方案可观察物和相图。 HarmonicBalance.jl是一款免费软件，请访问https://github.com/nonlinelearoscillations/harmonicbalance.jl。
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.
