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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · CriticalTransitions.jl</title><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>CriticalTransitions.jl</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a></li><li><a class="tocitem" href="quickstart/">Quickstart</a></li><li><a class="tocitem" href="tutorial/">Tutorial</a></li><li><span class="tocitem">Manual</span><ul><li><a class="tocitem" href="man/stochsystem/">Defining a StochSystem</a></li><li><a class="tocitem" href="man/systemanalysis/">Stability analysis</a></li><li><a class="tocitem" href="man/simulation/">Simulating the system</a></li><li><a class="tocitem" href="man/sampling/">Sampling transitions</a></li><li><a class="tocitem" href="man/largedeviations/">Large deviation theory</a></li><li><a class="tocitem" href="man/noise/">Noise processes</a></li><li><a class="tocitem" href="man/utils/">Utilities</a></li></ul></li><li><a class="tocitem" href="man/systems/">Predefined systems</a></li><li><a class="tocitem" href="man/dev/">Development stage</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/reykboerner/CriticalTransitions.jl/blob/main/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="CriticalTransitions.jl"><a class="docs-heading-anchor" href="#CriticalTransitions.jl">CriticalTransitions.jl</a><a id="CriticalTransitions.jl-1"></a><a class="docs-heading-anchor-permalink" href="#CriticalTransitions.jl" title="Permalink"></a></h1><p><em>A Julia package for the numerical investigation of noise- and rate-induced transitions in dynamical systems.</em></p><p>Building on <a href="https://juliadynamics.github.io/DynamicalSystems.jl/stable/">DynamicalSystems.jl</a> and <a href="https://diffeq.sciml.ai/stable/">DifferentialEquations.jl</a>, this package aims to provide a toolbox for dynamical systems under time-dependent forcing, with a focus on tipping phenomena and metastability.</p><div class="admonition is-compat"><header class="admonition-header">Compatibility</header><div class="admonition-body"><p>This version (<code>v0.2</code>) is now compatible with <code>DynamicalSystems v3</code>.</p></div></div><p><img src="figs/CTjl_structure.png" alt="CT.jl infographic"/></p><div class="admonition is-info"><header class="admonition-header">Current features</header><div class="admonition-body"><ul><li><strong>Stability analysis</strong>: Fixed points, linear stability, basins of attraction, edge tracking</li><li><strong>Stochastic simulation</strong>: Gaussian noise, uncorrelated and correlated, additive and multiplicative</li><li><strong>Transition path sampling</strong>: Ensemble sampling by direct simulation and Pathspace Langevin MCMC</li><li><strong>Large deviation theory</strong>: Action functionals and minimization algorithms (MAM, gMAM)</li></ul></div></div><div class="admonition is-category-ukw"><header class="admonition-header">Planned features</header><div class="admonition-body"><ul><li><strong>Rare event simulation</strong>: importance sampling, AMS</li><li><strong>Quasipotentials</strong>: Ordered line integral method (OLIM)</li><li><strong>Rate-induced tipping</strong> tools</li><li>...?</li></ul></div></div><p>Developers: Reyk Börner, Ryan Deeley and Raphael Römer</p><p>Thanks to Jeroen Wouters, Calvin Nesbitt, Tobias Grafke, George Datseris and Oliver Mehling</p><p>This work is part of the <a href="https://criticalearth.eu">CriticalEarth</a> project.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="quickstart/">Quickstart »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Friday 29 September 2023 17:32">Friday 29 September 2023</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · CriticalTransitions.jl</title><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>CriticalTransitions.jl</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a></li><li><a class="tocitem" href="quickstart/">Quickstart</a></li><li><a class="tocitem" href="tutorial/">Tutorial</a></li><li><span class="tocitem">Manual</span><ul><li><a class="tocitem" href="man/stochsystem/">Defining a StochSystem</a></li><li><a class="tocitem" href="man/systemanalysis/">Stability analysis</a></li><li><a class="tocitem" href="man/simulation/">Simulating the system</a></li><li><a class="tocitem" href="man/sampling/">Sampling transitions</a></li><li><a class="tocitem" href="man/largedeviations/">Large deviation theory</a></li><li><a class="tocitem" href="man/noise/">Noise processes</a></li><li><a class="tocitem" href="man/utils/">Utilities</a></li></ul></li><li><a class="tocitem" href="man/systems/">Predefined systems</a></li><li><a class="tocitem" href="man/dev/">Development stage</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/reykboerner/CriticalTransitions.jl/blob/main/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="CriticalTransitions.jl"><a class="docs-heading-anchor" href="#CriticalTransitions.jl">CriticalTransitions.jl</a><a id="CriticalTransitions.jl-1"></a><a class="docs-heading-anchor-permalink" href="#CriticalTransitions.jl" title="Permalink"></a></h1><p><em>A Julia package for the numerical investigation of noise- and rate-induced transitions in dynamical systems.</em></p><p>Building on <a href="https://juliadynamics.github.io/DynamicalSystems.jl/stable/">DynamicalSystems.jl</a> and <a href="https://diffeq.sciml.ai/stable/">DifferentialEquations.jl</a>, this package aims to provide a toolbox for dynamical systems under time-dependent forcing, with a focus on tipping phenomena and metastability.</p><div class="admonition is-compat"><header class="admonition-header">Compatibility</header><div class="admonition-body"><p>This version (<code>v0.2</code>) is now compatible with <code>DynamicalSystems v3</code>.</p></div></div><p><img src="figs/CTjl_structure.png" alt="CT.jl infographic"/></p><div class="admonition is-info"><header class="admonition-header">Current features</header><div class="admonition-body"><ul><li><strong>Stability analysis</strong>: Fixed points, linear stability, basins of attraction, edge tracking</li><li><strong>Stochastic simulation</strong>: Gaussian noise, uncorrelated and correlated, additive and multiplicative</li><li><strong>Transition path sampling</strong>: Ensemble sampling by direct simulation and Pathspace Langevin MCMC</li><li><strong>Large deviation theory</strong>: Action functionals and minimization algorithms (MAM, gMAM)</li></ul></div></div><div class="admonition is-category-ukw"><header class="admonition-header">Planned features</header><div class="admonition-body"><ul><li><strong>Rare event simulation</strong>: importance sampling, AMS</li><li><strong>Quasipotentials</strong>: Ordered line integral method (OLIM)</li><li><strong>Rate-induced tipping</strong> tools</li><li>...?</li></ul></div></div><p>Developers: Reyk Börner, Ryan Deeley and Raphael Römer</p><p>Thanks to Jeroen Wouters, Calvin Nesbitt, Tobias Grafke, George Datseris and Oliver Mehling</p><p>This work is part of the <a href="https://criticalearth.eu">CriticalEarth</a> project.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="quickstart/">Quickstart »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 31 January 2024 11:59">Wednesday 31 January 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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