如何用JiTCDDE实现多维时滞微分方程？

Question

我是一名用Python编写代码的学生，正在尝试求解以下延迟微分方程：

<a href="http://www.codecogs.com/eqnedit.php?latex=\left\{\begin{array}{l}\dot{v}(t)=&space;y(t)&space;\\&space;\dot{y}(t)=&space;\frac{a_1\alpha}{\omega_1}.y(t-\tau)).\{1-tanh^2[v(t-\tau)]\}&space;-&space;v(t)-\frac{1}{Q_1}.y(t)&space;\end{array}\right.\\&space;\\&space;(a_1&space;=&space;70,&space;\quad&space;Q_1&space;=&space;50,&space;\quad&space;\omega_1&space;=&space;2260,&space;\quad&space;\alpha&space;=&space;10,&space;\quad&space;\tau&space;\in&space;[0,8e-3])" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\left\{\begin{array}{l}\dot{v}(t)=&space;y(t)&space;\\&space;\dot{y}(t)=&space;\frac{a_1\alpha}{\omega_1}.y(t-\tau)).\{1-tanh^2[v(t-\tau)]\}&space;-&space;v(t)-\frac{1}{Q_1}.y(t)&space;\end{array}\right.\\&space;\\&space;(a_1&space;=&space;70,&space;\quad&space;Q_1&space;=&space;50,&space;\quad&space;\omega_1&space;=&space;2260,&space;\quad&space;\alpha&space;=&space;10,&space;\quad&space;\tau&space;\in&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])" /></a>

Answer 1

通过使用y的第一个参数来指示要使用哪个组件，可以实现多维系统。另外，微分方程右边的定义必须有两个分量。你知道吗

例如，您可以实现如下示例：

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)

在你的方程式中，v现在是y(0)；y变成了y(1)。你知道吗

在accompanying paper（preprint）中有一个二阶微分方程的例子。你知道吗