Quickstart

Installation

Although the package is not yet registered, you can install it from Github via the Julia package manager:

using Pkg; Pkg.add('https://github.com/juliadynamics/CriticalTransitions.jl.git')

The package is currently tested to be compatible with Julia versions 1.10 and 1.11.

Basic usage

The general workflow of CriticalTransitions essentially follows two steps:

Define your system as a CoupledSDEs (see Define a CoupledSDEs system)
Investigate the system by calling methods (see Methods)

New system type: RateSystem

We are planning to introduce the the struct RateSystem along CoupledSDEs. In a RateSystem, the time dependence of parameters can conveniently be specified, laying the foundation for a toolbox to study rate-induced tipping, or R-tipping.

Methods

Currently the following functions are implemented to analyze a CoupledSDEs and corresponding sample transition paths.

Attractors.bisect_to_edge
Attractors.edgetracking
ChaosTools.fixedpoints
CriticalTransitions.deterministic_orbit
CriticalTransitions.TransitionEnsemble
CriticalTransitions.TransitionStatistics
CriticalTransitions.transition
CriticalTransitions.transitions
CriticalTransitions.MinimumActionPath
CriticalTransitions.SgmamSystem
CriticalTransitions.action
CriticalTransitions.fw_action
CriticalTransitions.geometric_action
CriticalTransitions.geometric_min_action_method
CriticalTransitions.min_action_method
CriticalTransitions.om_action
CriticalTransitions.sgmam
CriticalTransitions.string_method
CriticalTransitions.div_drift
CriticalTransitions.drift
CriticalTransitions.intervals_to_box
CriticalTransitions.noise_process
CriticalTransitions.solver
StochasticSystemsBase.covariance_matrix
StochasticSystemsBase.diffusion_matrix