Duffing JavaScript integrator

This webpage uses the Runge-Kutta-Fehlberg fourth-order method with fifth-order error checking (RKF45) to approximate the solution to the problem of the Duffing oscillator: $$\ddot{x} + \delta \dot{x} + \alpha x + \beta x^3 = \gamma \cos{(\omega t)}$$ Below you can specify these various parameters, as well as the initial conditions and starting and end times. The default values give chaotic behaviour.

Parameter	Value	Explanation
$\alpha$:		Parameter.
$\beta$:		Parameter.
$\gamma$:		Parameter.
$\delta$:		Parameter.
$\omega$:		Parameter.
$t_0$:		Starting time for the simulation in seconds (s).
$t_f$:		End time for the simulation in seconds..
$x_0$:		x coordinate (in metres) at time $t_0$.
$\dot{x}_0$:		First derivative of $x$ with respect to $t$ at $t_0$ (in $\mathrm{metres}\cdot \mathrm{s}^{-1}$).
$\epsilon$:		Error tolerance in both $\theta$ and $\dot{\theta}$. $\epsilon \lt $2e-12 often freezes the webpage.
dtInitial:		Initial guess for step size.

Parameter	Value	Explanation
\(\alpha\):		Parameter.
\(\beta\):		Parameter.
\(\gamma\):		Parameter.
\(\delta\):		Parameter.
\(\omega\):		Parameter.
\(t_0\):		Starting time for the simulation in seconds (s).
\(t_f\):		End time for the simulation in seconds..
\(x_0\):		x coordinate (in metres) at time \(t_0\).
\(\dot{x}_0\):		First derivative of \(x\) with respect to \(t\) at \(t_0\) (in \(\mathrm{metres}\cdot \mathrm{s}^{-1}\)).
\(\epsilon\):		Error tolerance in both \(\theta\) and \(\dot{\theta}\). \(\epsilon \lt \)2e-12 often freezes the webpage.
dtInitial:		Initial guess for step size.