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:

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

where xx is the number of prey animals and yy is the number of predator animals and α,β,γ\alpha, \beta, \gamma, and δ\delta describe their interactions with one another.

Simulation parameter form.
Parameter Value Explanation
Natural growth rate of the population of prey animals.
The rate at which prey animals are killed by the predators.
The rate at which predator animals die in the absence of their prey.
The rate at which the population of predator animals increases due to the presence of their prey.
End time for the simulation in seconds.
Prey population.
Predator population.
Error tolerance.
Tolerance type, can be either absolute (0) or relative (1).
Initial step size.
Minimum allowed step size.
Time increment for skipping ahead in animation.
Time you want to skip ahead to in animation when you press the skip button.
Width (in px) of Plotly windows used for plotting and animation below.
Height (in px) of Plotly windows used for plotting and animation below.
Proportion of animation time passed per real time. tScale=1.0t_{\mathrm{Scale}}=1.0 means animation and real time match. tScale<1.0t_{\mathrm{Scale}}<1.0 means the animation is going more slowly than real time. tScale>1.0t_{\mathrm{Scale}}>1.0 means it is going more rapidly.