LyapunovExponents.jl --- A hackable Lyapunov exponents calculator

The aim of LyapunovExponents.jl is to provide an efficient research platform for computations related to Lyapunov exponents. This is (planned to be) achieved by exposing low-level APIs to Lyapunov exponents calculation.

At the moment, LyapunovExponents.jl is still at the very early stage of development and nowhere close to providing a stable API.

Features

Implemented:

• Lyapunov exponents calculation based on QR decomposition.
• Maximum Lyapunov exponent calculation.
• Covariant Lyapunov vectors calculation.
• Tangent space evolution based on the automatic differentiation tool ForwardDiff.jl.
• Testing utilities for tangent space evolution (Jacobian calculation) provided by users.
• Continuous dynamical systems support based on DifferentialEquations.jl. This means that the rich set of ODE solvers can be used.
• Random ordinary differential equation support.
• Various examples of continuous and discrete dynamical systems.
• OnlineStats.jl support: on-the-fly calculation of Lyapunov exponents, their variance, covariance, and any other statics it supports.
• (Experimental) Automatic termination.

Wanted list:

• Delay differential equations.
• Partial differential equations.
• Stochastic dynamical systems.
• Poincaré map.

Related works

• ChaosTools.jl from the DynamicalSystems.jl ecosystem is another Julia library which provides easy-to-use, clearly written, well-tested, and well-documented Lyapunov exponents calculation.
• eom is a Rust library which provides Lyapunov exponents and Covariant Lyapunov vectors calculation, on top of configurable ODE/PDE solvers.
• (I'm sure there are more...)

License

The LyapunovExponents.jl package is licensed under the MIT "Expat" License. See [LICENSE.md]() file.