Lotka-Volterra equations solver

This webpage uses the Runge-Kutta-Fehlberg fourth-order method with fifth-order error checking (RKF45) to approximate the solution to Lotka-Volterra equations:

\begin{aligned} \dfrac{dx}{dt} &= \alpha x - \beta xy \\ \dfrac{dy}{dt} &= \delta xy - \gamma y \end{aligned}

where $x$ is the number of prey animals and $y$ is the number of predator animals and $\alpha, \beta, \gamma$ , and $\delta$ describe their interactions with one another.

Simulation parameter form.
Parameter	Value	Explanation
$\alpha$ :		Natural growth rate of the population of prey animals.
$\beta$ :		The rate at which prey animals are killed by the predators.
$\gamma$ :		The rate at which predator animals die in the absence of their prey.
$\delta$ :		The rate at which the population of predator animals increases due to the presence of their prey.
$t_f$ :		End time for the simulation in seconds.
$x_0$ :		Prey population.
$y_0$ :		Predator population.
$\epsilon$ :		Error tolerance.
$\mathrm{Tol}_{\mathrm{type}}$ :		Tolerance type, can be either absolute (0) or relative (1).
$h_{\mathrm{Initial}}$ :		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.

© 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.

Lotka-Volterra equations solver

Mathematical simulation/solver pages

Complex analysis pages

Numerical mathematics

Lagrangian mechanics pages

Other mathematics

Education, my personal opinion largely

Linux