Lotka–Volterra equations (predator–prey equations) are used to model dynamical relationship between predators and they prey

## Introduction¶

Lotka-Volterra equations are used in simplest cases when there's only one predator population and one prey population. The model was developed in the beginning of 20^{th} century by Alfred Lotka and Vito Volterra (independently). https://en.wikipedia.org/wiki/Lotka-Volterra_equations

## Assumptions¶

- exponential growth of the prey population when the predator is absent
- the predator population will starve if the prey population is 0
- predators can consume infinite amount of prey
- environment is simple (both populations are moving randomly through a homogeneous environment)

## Model¶

Instead of using formulas to get the final value the model simulates all time steps to get historical data.

In [1]:

```
from iframer import *
iframer('https://statsim.com/app/?m=predatorprey&preview=1')
```