<p>You can implement multidimensional systems by using the first argument of <code>y</code> to indicate which component you want to use. Also, your definition of the right-hand side of the differential equation must have two components.</p>

<p>For instance, you can implement your example as follows:</p>

<pre><code>from jitcdde import jitcdde, y, t
f = [
        y(1),
        a*α/ω*y(1,t-τ)*(1-symengine.tanh(y(0,t-τ))**2)-y(0)-y(1)/Q
    ]

DDE = jitcdde(f)
</code></pre>

<p>What is <em>v</em> in your equation is now <code>y(0)</code>; <em>y</em> has become <code>y(1)</code>.</p>

<p>There is an example for a second-order differential equation such as yours in the <a href="http://dx.doi.org/10.1063/1.5019320" rel="nofollow noreferrer">accompanying paper</a> (<a href="https://arxiv.org/abs/1711.09886" rel="nofollow noreferrer">preprint</a>).</p>
How to implement a multidimensional delay differential equation with JiTCDDE?
<p>I'm a student coding in Python and trying to solve the folowing delayed differential equation:</p>

<p><div class="snippet" data-lang="js" data-hide="false" data-console="true" data-babel="false">
<div class="snippet-code">
<pre class="snippet-code-html lang-html prettyprint-override"><code>&lt;a href="http://www.codecogs.com/eqnedit.php?latex=\left\{\begin{array}{l}\dot{v}(t)=&amp;space;y(t)&amp;space;\\&amp;space;\dot{y}(t)=&amp;space;\frac{a_1\alpha}{\omega_1}.y(t-\tau)).\{1-tanh^2[v(t-\tau)]\}&amp;space;-&amp;space;v(t)-\frac{1}{Q_1}.y(t)&amp;space;\end{array}\right.\\&amp;space;\\&amp;space;(a_1&amp;space;=&amp;space;70,&amp;space;\quad&amp;space;Q_1&amp;space;=&amp;space;50,&amp;space;\quad&amp;space;\omega_1&amp;space;=&amp;space;2260,&amp;space;\quad&amp;space;\alpha&amp;space;=&amp;space;10,&amp;space;\quad&amp;space;\tau&amp;space;\in&amp;space;[0,8e-3])" target="_blank"&gt;&lt;img src="http://latex.codecogs.com/gif.latex?\left\{\begin{array}{l}\dot{v}(t)=&amp;space;y(t)&amp;space;\\&amp;space;\dot{y}(t)=&amp;space;\frac{a_1\alpha}{\omega_1}.y(t-\tau)).\{1-tanh^2[v(t-\tau)]\}&amp;space;-&amp;space;v(t)-\frac{1}{Q_1}.y(t)&amp;space;\end{array}\right.\\&amp;space;\\&amp;space;(a_1&amp;space;=&amp;space;70,&amp;space;\quad&amp;space;Q_1&amp;space;=&amp;space;50,&amp;space;\quad&amp;space;\omega_1&amp;space;=&amp;space;2260,&amp;space;\quad&amp;space;\alpha&amp;space;=&amp;space;10,&amp;space;\quad&amp;space;\tau&amp;space;\in&amp;space;[0,8e-3])" title="\left\{\begin{array}{l}\dot{v}(t)= y(t) \\ \dot{y}(t)= \frac{a_1\alpha}{\omega_1}.y(t-\tau)).\{1-tanh^2[v(t-\tau)]\} - v(t)-\frac{1}{Q_1}.y(t) \end{array}\right.\\ \\ (a_1 = 70, \quad Q_1 = 50, \quad \omega_1 = 2260, \quad \alpha = 10, \quad \tau \in [0,8e-3])" /&gt;&lt;/a&gt;</code></pre>
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</p>

<p>I wanted to use JiTCDDE, but didn’t succeed to find a way to adapt the system, even after studying the examples in the documentation of the module.
The major problem I have is that I don’t understand how to deal with the second equation containing <em>y</em> and <em>v</em> at the same time.</p>

<p>The goal is to plot the bifurcation diagram of the system (<em>v</em> as a function of <em>τ</em>). Am I using the wrong tool? Or is there a way to use JiTCDDE in my situation?</p>