The [url=https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations]Lotka-Volterra equations[/url] (also known as the predator-prey equations) are a pair of first-order non-linear differential equations. They are used to describe the dynamics of biological systems in which two species interact, one as a predator (here foxes) and the other as prey (here rabbits). The populations change through time according to the equation system: [math]x' = a x - b x y, y' = d x y - c y[/math] where [i]a[/i], [i]b[/i], [i]c[/i] and [i]d[/i] are some given constants.[br]Use the "play" button in the bottom-left corner to start visualizing the system. You can learn how the system behaves if you drag the moving point in the coordinate system, or you can set completely new values for the constants on the right.

Credits: Descriptive texts were taken from A. B. Çambel's book [url=http://www.goodreads.com/book/show/154279.Applied_Chaos_Theory]Applied Chaos Theory: A Paradigm for Complexity[/url]. Clipart images were copied from [url=http://openclipart.org]openclipart[/url].