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{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-10-26T15:21:26","documenter_version":"1.7.0"}}
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Function</a></li><li><a class="tocitem" href="../../../comparison/">Comparison</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"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Fractional Order Arneodo System</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Fractional Order Arneodo System</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/SciFracX/FractionalDiffEq.jl/blob/master/docs/ChaosGallery/Gallery/Arneodo.md#" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Fractional-Order-Arneodo-System"><a class="docs-heading-anchor" href="#Fractional-Order-Arneodo-System">Fractional Order Arneodo System</a><a id="Fractional-Order-Arneodo-System-1"></a><a class="docs-heading-anchor-permalink" href="#Fractional-Order-Arneodo-System" title="Permalink"></a></h1><pre><code class="language-julia hljs">using FractionalDiffEq, Plots

h=0.005
alpha = [0.97, 0.97, 0.96]
x0 = [-0.2, 0.5, 0.2]
tspan = (0, 100)
function Arneodo!(du, u, p, t)
b1, b2, b3, b4 = -5.5, 3.5, 0.8, -1.0
du[1] = u[2]
du[2] = u[3]
du[3] = -b1*u[1]-b2*u[2]-b3*u[3]+b4*u[1]^3
end
prob = FODESystem(Arneodo!, alpha, x0, tspan)
sol = solve(prob, h, GL())

plot(sol, vars=(1,2,3), title=&quot;Fractional Order Arneodo System&quot;)</code></pre><p><img src="../assets/Arneodo.png" alt="Arneodo"/></p><hr/><p><em>This page was generated using <a href="https://github.com/JuliaDocs/DemoCards.jl">DemoCards.jl</a>.</em></p></article><nav class="docs-footer"><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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Saturday 26 October 2024 15:21">Saturday 26 October 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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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><link href="../../../assets/favicon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../../"><img src="../../../assets/logo.svg" alt="FractionalDiffEq.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../../../">FractionalDiffEq.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../../../">FractionalDiffEq.jl</a></li><li><a class="tocitem" href="../../../get_started/">Get Started</a></li><li><a class="tocitem" href="../../../multiterm/">Multi-terms Fractional Differential Equations</a></li><li><a class="tocitem" href="../../../fdesystem/">System of Fractional Differential Equations</a></li><li><a class="tocitem" href="../../../fdde/">Fractional Delay Differential Equations</a></li><li><a class="tocitem" href="../../../dode/">Distributed Order Differential Equations</a></li><li><a class="tocitem" href="../../../discrete/">Fractional Differences Equations</a></li><li><a class="tocitem" href="../../../ffode/">Fractal-Fractional Differential Equations</a></li><li><a class="tocitem" href="../../../flyapunovexp/">Lyapunov Exponents</a></li><li><a class="tocitem" href="../../../ode/">Ordinary Differential Equations</a></li><li><a class="tocitem" href="../../">Fractional Order Chaos Gallery</a></li><li><a class="tocitem" href="../../../problems/">Problems</a></li><li><a class="tocitem" href="../../../algorithms/">Algorithms</a></li><li><a class="tocitem" href="../../../mittagleffler/">Mittag Leffler Function</a></li><li><a class="tocitem" href="../../../comparison/">Comparison</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"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Fractional Order Brusselator System</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Fractional Order Brusselator System</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/SciFracX/FractionalDiffEq.jl/blob/master/docs/ChaosGallery/Gallery/Brusselator.md#" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Fractional-Order-Brusselator-System"><a class="docs-heading-anchor" href="#Fractional-Order-Brusselator-System">Fractional Order Brusselator System</a><a id="Fractional-Order-Brusselator-System-1"></a><a class="docs-heading-anchor-permalink" href="#Fractional-Order-Brusselator-System" title="Permalink"></a></h1><p class="math-container">\[\begin{cases}
{_{t_0}D_t^\alpha}y_1(t)=a-(\mu+1)y_1(t)+(y_1(t))^2y_2(t)\\
{_{t_0}D_t^\alpha}y_2(t)=\mu y_1(t)-(y_1(t))^2y_2(t)\\
y_1(t_0)=y_{1,0}\\
y_2(t_0)=y_{2,0}
\end{cases}\]</p><pre><code class="language-julia hljs">using FractionalDiffEq, Plots

α = [0.8, 0.8]
u0 = [0.2, 0.03]
h = 0.001
tspan = (0, 100)

function Brusselator!(du, u, p, t)
a, μ = 1, 4
du[1] = a-(μ+1)*u[1]+(u[1])^2*u[2]
du[2] = μ*u[1]-(u[1])^2*u[2]
end

prob = FODEProblem(Brusselator!, α, u0, tspan)
sol = solve(prob, h, GL())

# Phase plane
plot(sol, vars=(1,2))

# Time plane
plot(sol, vars=(0,1,2))</code></pre><p><img src="../assets/Brusselator.png" alt="BrusselatorPhase"/></p><p><img src="../assets/BrusselatorTime.png" alt="BrusselatorTime"/></p><hr/><p><em>This page was generated using <a href="https://github.com/JuliaDocs/DemoCards.jl">DemoCards.jl</a>.</em></p></article><nav class="docs-footer"><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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Saturday 26 October 2024 15:21">Saturday 26 October 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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