Rabinovich–Fabrikant equations solver

This webpage uses the Runge-Kutta-Fehlberg fourth-order method with fifth-order error checking (RKF45) to approximate the solution to Rabinovich–Fabrikant equations

\begin{aligned} \dfrac{dx}{dt} &= y(z-1+x^2) + \gamma x \\ \dfrac{dy}{dt} &= x (3z+1-x^2) + \gamma y \\ \dfrac{dz}{dt} &= -2z(\alpha+xy). \end{aligned}

Simulation parameter form.
Parameter	Value	Explanation
$\alpha$ :		Problem parameter
$\gamma$ :		Problem parameter
$t_f$ :		End time for the simulation in seconds (s)
$x_0$ :		Initial $x$ coordinate.
$y_0$ :		Initial $y$ coordinate.
$z_0$ :		Initial $z$ coordinate.
$\epsilon$ :		Absolute error tolerance.
$h_{\mathrm{Initial}}$ :		Initial step size.
$h_{\mathrm{Min}}$ :		Minimum allowed step size.
$\Delta t$ :		Time increment for skipping ahead in animation.
$t_1$ :		Time you want to skip ahead to in animation when you press the skip button.
$\mathrm{Width}$ :		Width (in px) of Plotly windows used for plotting and animation below.
$\mathrm{Height}$ :		Height (in px) of Plotly windows used for plotting and animation below.
$t_\mathrm{Scale}$ :		Proportion of animation time passed per real time. $t_{\mathrm{Scale}}=1.0$ means animation and real time match. $t_{\mathrm{Scale}}<1.0$ means the animation is going more slowly than real time. $t_{\mathrm{Scale}}>1.0$ means it is going more rapidly.
$\mathrm{Opacity}$ :		Opacity of the lines in the 3D phase space animation. Customizable in case you need to tweak it in order to see the red dot marker.

© Brenton Horne. I do not claim to be infallible, so feel free to open issues or pull requests on GitHub if you notice flaws or things that can be improved.
I favour Oxford spelling, so if you notice I generally use different spelling to Australian spelling, that is probably why.
Homepage. Source code: https://github.com/fusion809/fusion809.github.io.
Website built with Franklin.jl.

Rabinovich–Fabrikant equations solver

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