2026-08-13 –, Tent — RW1
The DynamicalSystems.jl library allows analyzing nonlinear dynamical systems in Julia. However, functionality for systems with random or time-dependent forcing has been limited. Extending the existing interface to include coupled stochastic differential equations and nonautonomous systems, we introduce CriticalTransitions.jl: a user-friendly, well-documented package of numerical methods from large deviations and dynamical systems theory to simulate and understand critical behavior, e.g. tipping.
Metastability and tipping phenomena are important features of nonlinear dynamical systems in the natural and human world. CriticalTransitions.jl provides tools in a familiar user interface that allow to study such behavior.
We discuss the structure, functionality and intuitive interface of the package, closely following the way dynamical systems theory would be written in textbooks. The code builds on, and naturally integrates with, the well-established packages DynamicalSystems.jl and DifferentialEquations.jl, ensuring proven long-term reliability and compatibility.
By means of two example systems, we demonstrate the basic usage of CriticalTransitions.jl:
- Noise-induced transitions
Set up a ‘CoupledSDEs’ (a system of stochastic differential equations)
Compute its minimum-action path (“instanton”) between two attractors
Efficiently sample ensembles of noise-induced transition paths;
- Rate-induced transitions
Set up a ‘RateSystem’ by applying a time-dependent parametric forcing to a given system
Sample rate-induced transitions and calculate critical rates
Visualize the morphing stability landscape as a function of the forcing.
Postdoctoral researcher at the Institute for Marine and Atmospheric research Utrecht, Utrecht University, working at the interface between dynamical systems theory, complexity science and climate dynamics.