Getting started

Installation

To install the Julia language, we recommend juliaup.

CriticalTransitions is a registered Julia package (as of v0.7) and can be installed with the Julia package manager:

julia> ]
Pkg>   add CriticalTransitions

or

using Pkg; Pkg.add("CriticalTransitions")

The package is currently tested to be compatible with Julia versions 1.10-1.12.

Basic usage

The general workflow of CriticalTransitions.jl consists of two steps, similar to DynamicalSystems.jl:

1. Define your dynamical system (see Defining a forced dynamical system)
2. Investigate the system by calling methods (see Index)

Some methods are only loaded as extensions when loading other dependency packages (see Extensions).

Documentation

The Tutorial and code examples in the Examples section illustrate some use cases of the package. All available methods and types are documented in the Manual section (see Index for an overview).

Index

A quick overview of available features:

Defining a system and its forcing

• DynamicalSystemsBase.CoupledODEs
• DynamicalSystemsBase.CoupledSDEs (alias for StochSystem)
• CriticalTransitions.RateSystem
• CriticalTransitions.ForcingProfile

System analysis and simulation

• Attractors.EdgeTrackingResults
• Attractors.bisect_to_edge
• Attractors.edgetracking
• ChaosTools.fixedpoints
• CriticalTransitions.deterministic_orbit
• DynamicalSystemsBase.trajectory

Stochastic dynamics: Transition path sampling, large deviation theory

• 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

Nonautonomous dynamics: Rate-induced tipping

More

• CriticalTransitions.intervals_to_box

Extensions

• Loading the ChaosTools dependency makes the functions fixedpoints and intervals_to_box available.

using CriticalTransitions
using ChaosTools

# Now the following functions are available
fixedpoints()
intervals_to_box()

• Loading the Attractors dependency makes the functions edgetracking and bisect_to_edge available.

using CriticalTransitions
using Attractors

# Now the following functions are available
edgetracking()
bisect_to_edge()